1:"$Sreact.fragment"
2:I[10156,[],""]
3:I[6746,[],""]
4:I[76837,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","104","static/chunks/104-e8a10a728f64230d.js","3374","static/chunks/3374-cffcb39c106cc278.js","6344","static/chunks/6344-f0148458c0499269.js","2043","static/chunks/2043-cb8fa44c52a8f8b9.js","9559","static/chunks/app/(frontend)/layout-42f64306bd0733c5.js"],"default"]
5:I[32043,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","104","static/chunks/104-e8a10a728f64230d.js","3374","static/chunks/3374-cffcb39c106cc278.js","6344","static/chunks/6344-f0148458c0499269.js","2043","static/chunks/2043-cb8fa44c52a8f8b9.js","9559","static/chunks/app/(frontend)/layout-42f64306bd0733c5.js"],"default"]
6:I[67821,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","6956","static/chunks/66a6e935-aee5d3cb85c323ac.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","9858","static/chunks/9858-f1918ded0530ca69.js","609","static/chunks/609-95e41ae6a69b88b2.js","2456","static/chunks/2456-94cb89c116d69dd0.js","994","static/chunks/994-2c56ebb2d663b523.js","6472","static/chunks/6472-2ee935ddbae5821a.js","3349","static/chunks/app/(frontend)/calculators/%5Bcategory%5D/%5Bslug%5D/page-70bb6ad84377852d.js"],""]
1a:I[14600,[],"default",1]
:HL["/_next/static/media/849c382dee069680-s.p.woff2","font",{"crossOrigin":"","type":"font/woff2"}]
:HL["/_next/static/media/e4af272ccee01ff0-s.p.woff2","font",{"crossOrigin":"","type":"font/woff2"}]
:HL["/_next/static/css/60d9b09af57ce3c6.css","style"]
:HL["/_next/static/css/9c59f2e83b7f05d1.css","style"]
0:{"P":null,"c":["","calculators","math","lcd-calculator.rsc"],"q":"","i":false,"f":[[["",{"children":["(frontend)",{"children":["calculators",{"children":[["category","math","d",null],{"children":[["slug","lcd-calculator","d",null],{"children":["__PAGE__",{}]}]}]}]},"$undefined","$undefined",16]}],[["$","$1","c",{"children":[null,["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":[[["$","title",null,{"children":"404: This page could not be found."}],["$","div",null,{"style":{"fontFamily":"system-ui,\"Segoe UI\",Roboto,Helvetica,Arial,sans-serif,\"Apple Color Emoji\",\"Segoe UI Emoji\"","height":"100vh","textAlign":"center","display":"flex","flexDirection":"column","alignItems":"center","justifyContent":"center"},"children":["$","div",null,{"children":[["$","style",null,{"dangerouslySetInnerHTML":{"__html":"body{color:#000;background:#fff;margin:0}.next-error-h1{border-right:1px solid rgba(0,0,0,.3)}@media (prefers-color-scheme:dark){body{color:#fff;background:#000}.next-error-h1{border-right:1px solid rgba(255,255,255,.3)}}"}}],["$","h1",null,{"className":"next-error-h1","style":{"display":"inline-block","margin":"0 20px 0 0","padding":"0 23px 0 0","fontSize":24,"fontWeight":500,"verticalAlign":"top","lineHeight":"49px"},"children":404}],["$","div",null,{"style":{"display":"inline-block"},"children":["$","h2",null,{"style":{"fontSize":14,"fontWeight":400,"lineHeight":"49px","margin":0},"children":"This page could not be found."}]}]]}]}]],[]],"forbidden":"$undefined","unauthorized":"$undefined"}]]}],{"children":[["$","$1","c",{"children":[[["$","link","0",{"rel":"stylesheet","href":"/_next/static/css/60d9b09af57ce3c6.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","link","1",{"rel":"stylesheet","href":"/_next/static/css/9c59f2e83b7f05d1.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}]],["$","html",null,{"lang":"en","data-scroll-behavior":"smooth","children":[["$","body",null,{"className":"bg-white antialiased dark:bg-mist-950 __variable_f367f3 __variable_008b00","suppressHydrationWarning":true,"children":[["$","div",null,{"className":"flex min-h-screen flex-col justify-between","children":[["$","$L4",null,{}],["$","$L5",null,{"children":["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":[["$","main",null,{"className":"isolate overflow-clip","children":["$","section",null,{"className":"py-16","children":["$","div",null,{"className":"mx-auto w-full max-w-2xl px-6 md:max-w-3xl lg:max-w-7xl lg:px-10 flex flex-col items-center gap-6","children":[["$","h1",null,{"className":"font-display text-5xl/12 tracking-tight text-balance sm:text-[5rem]/20 text-mist-950 dark:text-white max-w-5xl text-center","children":"Page not found"}],["$","div",null,{"className":"text-lg/8 text-mist-700 dark:text-mist-400 max-w-xl text-center","children":["$","p",null,{"children":"Sorry, the page you were looking for could not be found."}]}],["$","$L6",null,{"href":"/","className":"inline-flex items-center gap-2 text-sm/7 font-medium text-mist-950 dark:text-white","children":["Go back home ",["$","svg",null,{"width":13,"height":7,"viewBox":"0 0 13 7","fill":"none","strokeWidth":1,"role":"image","className":"inline-block","children":[["$","path",null,{"d":"M12.5049 3.49512L0.504883 3.49512","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round"}],["$","path",null,{"d":"M9.5 6.5L12.5 3.5L9.5 0.5","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round"}]]}]]}]]}]}]}],[]],"forbidden":"$undefined","unauthorized":"$undefined"}]}],["$","footer",null,{"children":["$","div",null,{"className":"bg-mist-950/2.5 py-16 text-mist-950 dark:bg-white/5 dark:text-white","children":["$","div",null,{"className":"mx-auto w-full max-w-2xl px-6 md:max-w-3xl lg:max-w-7xl lg:px-10 flex flex-col gap-12","children":[["$","div",null,{"className":"flex flex-col items-start justify-between gap-6 sm:flex-row","children":[["$","div",null,{"className":"flex flex-col items-start gap-2","children":[["$","$L6",null,{"href":"/","children":["$","svg",null,{"className":"h-5 w-auto","xmlns":"http://www.w3.org/2000/svg","width":742,"height":68,"viewBox":"0 0 742 68","fill":"none","children":[["$","path",null,{"fill":"#161616","d":"M129.5 41.4c0-13 10.5-23.4 23.4-23.4 12.9 0 23.3 10.4 23.3 23.4v22.7h-11.8v-4.8c-1.4 3-6.3 5.5-11.5 5.5-12.9 0-23.4-10.4-23.4-23.4Zm35 0c0-6.7-4.8-11.9-11.5-11.9s-11.7 5.2-11.7 11.9 5 11.9 11.7 11.9c6.7 0 11.5-5.2 11.5-11.9ZM181.2 41.4c0-13 10.4-23.4 23.4-23.4 13 0 19.8 7.2 22.5 16.9h-12.5c-2-3.3-5.5-5.4-9.9-5.4-6.7 0-11.7 5.2-11.7 11.9s5 11.9 11.7 11.9c6.7 0 7.4-2 9.5-5H227c-2.9 9.6-11.8 16.5-22.4 16.5-10.6 0-23.4-10.4-23.4-23.4ZM248.3 30.3v12.4c0 7.3 2.4 10.2 8.2 10.2v11.5c-11.6 0-19.9-6.4-19.9-21.7V30.3h-6.7V18.8h6.6V1.1h11.8v17.7h8.3v11.5H248.3ZM274 18.7h-11.8V64H274V18.7ZM277.8 18.7h12.3l10.3 29.8 10.4-29.8h12.3L306.2 64h-11.8l-16.8-45.3h.2ZM345.8 18c11.2 0 23.2 8 23.7 22.4 0 2.1 0 4.1-.4 5.6h-33.6c1.1 4.5 5.1 7.3 10.3 7.3 5.2 0 6.3-1.5 7.8-2.6h14c-3.6 8.3-11.9 14.1-21.5 14.1s-23.4-10.4-23.4-23.3 10-23.5 23-23.5h.1Zm11 18.6c-1.8-4.3-6.2-7.1-10.7-7.1-4.5 0-8.9 2.8-10.7 7.1h21.4Z"}],"$L7","$L8","$L9","$La","$Lb","$Lc"]}]}],"$Ld"]}],"$Le"]}],"$Lf","$L10"]}]}]}]]}],"$L11","$L12"]}],"$L13"]}]]}],{"children":["$L14",{"children":["$L15",{"children":["$L16",{"children":["$L17",{},null,false,null]},null,false,"$@18"]},null,false,"$@18"]},null,false,"$@18"]},null,false,null]},null,false,"$@18"],"$L19",false]],"m":"$undefined","G":["$1a",[]],"S":true,"h":null,"b":"qKrY2dUw1szY2xJfsSyIe"}
1c:I[14245,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","104","static/chunks/104-e8a10a728f64230d.js","3374","static/chunks/3374-cffcb39c106cc278.js","6344","static/chunks/6344-f0148458c0499269.js","2043","static/chunks/2043-cb8fa44c52a8f8b9.js","9559","static/chunks/app/(frontend)/layout-42f64306bd0733c5.js"],"Button"]
22:I[46726,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","104","static/chunks/104-e8a10a728f64230d.js","3374","static/chunks/3374-cffcb39c106cc278.js","6344","static/chunks/6344-f0148458c0499269.js","2043","static/chunks/2043-cb8fa44c52a8f8b9.js","9559","static/chunks/app/(frontend)/layout-42f64306bd0733c5.js"],"default"]
23:I[19592,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","6956","static/chunks/66a6e935-aee5d3cb85c323ac.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","9858","static/chunks/9858-f1918ded0530ca69.js","609","static/chunks/609-95e41ae6a69b88b2.js","6344","static/chunks/6344-f0148458c0499269.js","2456","static/chunks/2456-94cb89c116d69dd0.js","994","static/chunks/994-2c56ebb2d663b523.js","6472","static/chunks/6472-2ee935ddbae5821a.js","2018","static/chunks/app/(frontend)/%5B...slug%5D/page-dcf70230194846a1.js"],""]
24:I[79066,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","6956","static/chunks/66a6e935-aee5d3cb85c323ac.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","9858","static/chunks/9858-f1918ded0530ca69.js","609","static/chunks/609-95e41ae6a69b88b2.js","6344","static/chunks/6344-f0148458c0499269.js","2456","static/chunks/2456-94cb89c116d69dd0.js","994","static/chunks/994-2c56ebb2d663b523.js","6472","static/chunks/6472-2ee935ddbae5821a.js","2018","static/chunks/app/(frontend)/%5B...slug%5D/page-dcf70230194846a1.js"],"GoogleTagManager"]
26:I[85305,[],"OutletBoundary"]
27:"$Sreact.suspense"
2a:I[85305,[],"ViewportBoundary"]
2c:I[85305,[],"MetadataBoundary"]
1b:T5a9,M373.9 41.4c0-13 10.5-23.4 23.4-23.4 12.9 0 16.9 5.3 20.6 12.8h-6.3c-3.2-4.4-8.2-7.3-14.2-7.3-10 0-17.7 7.9-17.7 17.9 0 10 7.9 17.9 17.7 17.9 9.8 0 11.1-3 14.2-7.3h6.4c-3.7 7.6-11.6 12.9-20.8 12.9-9.2 0-23.4-10.4-23.4-23.4l.1-.1ZM422.7 41.4c0-13 10.5-23.4 23.4-23.4 12.9 0 23.3 10.4 23.3 23.4v22.7h-5.8v-9.7c-3 6-9.8 10.4-17.5 10.4-12.9 0-23.4-10.4-23.4-23.4Zm41 0c0-10-7.5-17.9-17.5-17.9s-17.7 7.9-17.7 17.9c0 10 7.9 17.9 17.7 17.9 9.8 0 17.5-7.9 17.5-17.9ZM475.7 64.1V.7h5.8v63.4h-5.8ZM486.5 41.4c0-13 10.5-23.4 23.4-23.4 12.9 0 16.9 5.3 20.6 12.8h-6.3c-3.2-4.4-8.2-7.3-14.2-7.3-10 0-17.7 7.9-17.7 17.9 0 10 7.9 17.9 17.7 17.9 9.8 0 11.1-3 14.2-7.3h6.4c-3.7 7.6-11.6 12.9-20.8 12.9-9.2 0-23.4-10.4-23.4-23.4l.1-.1ZM575.6 18.7v23.8c0 15.2-8.3 22.2-19.9 22.2-11.6 0-19.9-7-19.9-22.2V18.7h5.8v23.8c0 11.3 5.7 16.7 14.1 16.7 8.4 0 14.1-5.3 14.1-16.7V18.7h5.8ZM581.9 64.1V.7h5.8v63.4h-5.8ZM592.7 41.4c0-13 10.5-23.4 23.4-23.4 12.9 0 23.3 10.4 23.3 23.4v22.7h-5.8v-9.7c-3 6-9.8 10.4-17.5 10.4-12.9 0-23.4-10.4-23.4-23.4Zm41 0c0-10-7.5-17.9-17.5-17.9s-17.7 7.9-17.7 17.9c0 10 7.9 17.9 17.7 17.9 9.8 0 17.5-7.9 17.5-17.9ZM652.5 24.3v18.2c0 10.1 4.4 15.1 11.4 16.2v5.6c-10.2-1-17.2-7.8-17.2-21.7V24.2h-6.8v-5.5h6.8V4.4h5.8v14.3h11.4v5.5h-11.4v.1ZM712 41.4c0 13-10.4 23.4-23.4 23.4-13 0-23.4-10.4-23.4-23.4 0-13 10.5-23.4 23.4-23.4 12.9 0 23.4 10.4 23.4 23.4Zm-41 0c0 10 7.9 17.9 17.7 17.9 9.8 0 17.5-7.9 17.5-17.9 0-10-7.5-17.9-17.5-17.9S671 31.4 671 41.4Z7:["$","path",null,{"fill":"#262626","d":"$1b"}]
8:["$","path",null,{"fill":"#09C269","d":"M274 1.1h-11.8v11.8H274V1.1Z"}]
9:["$","path",null,{"fill":"#161616","d":"M248.2 1.1v17.6L236.4 1.1h11.8Z"}]
a:["$","path",null,{"fill":"#09C269","d":"M65.2 47.1c-4.1-5.4-2.8-11.8-4.4-18-1.1-4.2-3.1-8.2-5.8-11.6-.7-.9-1.5-1.8-2.3-2.6-5.6-5.6-13.3-9-21.8-9C13.1 5.9-1.1 21 .2 39c1.3 18 13 26.9 27.9 28.2 9.6.8 18.4-2.8 24.6-9l-.4-.4c-3-3.8-5.1-8-6.3-12.6-3.3 5.7-9.7 9.4-16.8 8.7-8.1-.8-14.7-7.3-15.6-15.3-.9-8 7-19.4 17.3-19.4S43 22.7 46 27.9c2.6 4.6 2 9.6 3 14.6.9 4.8 2.9 9.3 6 13.2 5.6 7.1 14.3 11.6 24 11.6h30.8V55.2H82.1c-6.3 0-12.4-2.7-16.4-7.5-.2-.2-.4-.5-.6-.7l.1.1Z"}]
b:["$","path",null,{"fill":"#09C269","d":"M64 27.9c3-5.2 8.6-8.8 15.1-8.8 9.6 0 17.4 7.8 17.4 17.4h13.4c0-17-13.8-30.8-30.8-30.8s-16.2 3.5-21.8 9.1l.4.5c3 3.8 5.1 8 6.3 12.6Z"}]
c:["$","path",null,{"fill":"#262626","d":"M717.3 40.6c0-15.5 7.9-22.6 19.1-22.6h1.4v5.7h-1.4c-7.8 0-13.1 5.4-13.1 16.9v24.2h-6V40.6Z"}]
d:["$","p",null,{"className":"text-sm text-mist-600 dark:text-mist-400","children":"Interactive calculators that convert visitors into leads."}]
e:["$","$L1c",null,{"el":"a","href":"https://app.activecalculator.com/auth/signup","appearance":"default","label":"Get started free","data-umami-event":"click-cta-footer","data-umami-event-location":"footer"}]
f:["$","nav",null,{"className":"grid grid-cols-2 gap-6 text-sm/7 md:grid-cols-4","children":[["$","div","Use Cases",{"children":[["$","h3",null,{"children":"Use Cases"}],["$","ul",null,{"role":"list","className":"mt-2 flex flex-col gap-2","children":[["$","li","E-Commerce & Retail",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/templates/category/e-commerce","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"E-Commerce & Retail"}]}],["$","li","Finance",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/templates/category/finance","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Finance"}]}],["$","li","Unit Conversion",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/templates/category/unit-conversion","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Unit Conversion"}]}],["$","li","Price Quote",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/templates/category/price-quote","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Price Quote"}]}]]}],[["$","div","Industries",{"className":"mt-6","children":[["$","h3",null,{"children":"Industries"}],["$","ul",null,{"role":"list","className":"mt-2 flex flex-col gap-2","children":[["$","li","Screen Printing",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/industries/screen-printing","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Screen Printing"}]}],["$","li","Mortgage Brokers",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/industries/mortgage-brokers","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Mortgage Brokers"}]}],["$","li","Solar Energy",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/industries/solar-energy","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Solar Energy"}]}]]}]]}]]]}],["$","div","Templates",{"children":[["$","h3",null,{"children":"Templates"}],["$","ul",null,{"role":"list","className":"mt-2 flex flex-col gap-2","children":[["$","li","Ad Spend ROI Calculator",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/templates/ad-spend-roi-calculator","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Ad Spend ROI Calculator"}]}],["$","li","Amortization Payment Calculator Canada",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/templates/amortization-payment-calculator-canada","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Amortization Payment Calculator Canada"}]}],["$","li","Amortization Calculator",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/templates/amortization-calculator","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Amortization Calculator"}]}],["$","li","Balloon Loan Calculator Lead Gen",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/templates/balloon-loan-calculator-lead-gen","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Balloon Loan Calculator Lead Gen"}]}]]}],"$undefined"]}],["$","div","Product",{"children":[["$","h3",null,{"children":"Product"}],["$","ul",null,{"role":"list","className":"mt-2 flex flex-col gap-2","children":[["$","li","Templates",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/templates","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Templates"}]}],["$","li","Calculators",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/calculators","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Calculators"}]}],["$","li","Pricing",{"className":"text-mist-700 dark:text-mist-400","children":"$L1d"}],"$L1e","$L1f","$L20"]}],"$undefined"]}],"$L21"]}]
10:["$","div",null,{"className":"flex flex-col items-start justify-between gap-4 border-t border-mist-950/10 pt-8 text-sm/7 sm:flex-row sm:items-center dark:border-white/10","children":[["$","div",null,{"className":"flex flex-wrap items-center gap-x-4 gap-y-1 text-mist-600 dark:text-mist-500","children":[["$","span",null,{"children":["© ",2026," ActiveCalculator."]}],[["$","$L6","Privacy Policy",{"href":"/privacy","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Privacy Policy"}],["$","$L6","Terms of Service",{"href":"/terms","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Terms of Service"}]]]}],["$","div",null,{"className":"flex items-center gap-4","children":[["$","a","X",{"href":"https://twitter.com/activecalculator","target":"_blank","rel":"noopener noreferrer","aria-label":"X","data-umami-event":"click-social","data-umami-event-location":"footer","data-umami-event-target":"x","className":"text-mist-600 transition-colors *:size-5 hover:text-mist-950 dark:text-mist-500 dark:hover:text-white","children":["$","svg",null,{"width":24,"height":24,"viewBox":"0 0 24 24","fill":"currentColor","role":"image","className":"inline-block","children":["$","path",null,{"d":"M13.6833 10.6218L20.2401 3H18.6864L12.9931 9.61788L8.44583 3H3.20117L10.0775 13.0074L3.20117 21H4.75501L10.7673 14.0113L15.5695 21H20.8141L13.6833 10.6218ZM11.5551 13.0956L10.8584 12.0991L5.31488 4.16971H7.7015L12.1752 10.5689L12.8719 11.5655L18.6871 19.8835H16.3005L11.5551 13.0956Z"}]}]}],["$","a","LinkedIn",{"href":"https://linkedin.com/company/activecalculator","target":"_blank","rel":"noopener noreferrer","aria-label":"LinkedIn","data-umami-event":"click-social","data-umami-event-location":"footer","data-umami-event-target":"linkedin","className":"text-mist-600 transition-colors *:size-5 hover:text-mist-950 dark:text-mist-500 dark:hover:text-white","children":["$","svg",null,{"width":24,"height":24,"viewBox":"0 0 24 24","fill":"currentColor","role":"image","className":"inline-block","children":["$","path",null,{"d":"M20.447 20.452h-3.554v-5.569c0-1.328-.027-3.037-1.852-3.037-1.853 0-2.136 1.445-2.136 2.939v5.667H9.351V9h3.414v1.561h.046c.477-.9 1.637-1.85 3.37-1.85 3.601 0 4.267 2.37 4.267 5.455v6.286zM5.337 7.433a2.062 2.062 0 01-2.063-2.065 2.064 2.064 0 112.063 2.065zm1.782 13.019H3.555V9h3.564v11.452zM22.225 0H1.771C.792 0 0 .774 0 1.729v20.542C0 23.227.792 24 1.771 24h20.451C23.2 24 24 23.227 24 22.271V1.729C24 .774 23.2 0 22.222 0h.003z"}]}]}],["$","a","YouTube",{"href":"https://youtube.com/@activecalculator","target":"_blank","rel":"noopener noreferrer","aria-label":"YouTube","data-umami-event":"click-social","data-umami-event-location":"footer","data-umami-event-target":"youtube","className":"text-mist-600 transition-colors *:size-5 hover:text-mist-950 dark:text-mist-500 dark:hover:text-white","children":["$","svg",null,{"width":24,"height":24,"viewBox":"0 0 24 24","fill":"currentColor","role":"image","className":"inline-block","children":["$","path",null,{"fillRule":"evenodd","d":"M19.812 5.418c.861.23 1.538.907 1.768 1.768C21.998 8.746 22 12 22 12s0 3.255-.418 4.814a2.504 2.504 0 0 1-1.768 1.768c-1.56.419-7.814.419-7.814.419s-6.255 0-7.814-.419a2.505 2.505 0 0 1-1.768-1.768C2 15.255 2 12 2 12s0-3.255.417-4.814a2.507 2.507 0 0 1 1.768-1.768C5.744 5 11.998 5 11.998 5s6.255 0 7.814.418ZM15.194 12 10 15V9l5.194 3Z","clipRule":"evenodd"}]}]}]]}]]}]
11:["$","$L22",null,{}]
12:["$","$L23",null,{"defer":true,"src":"https://analytics.selvo.co/script.js","data-website-id":"20975f57-f91a-4d7f-a72e-bc1f75a733ed","strategy":"afterInteractive"}]
13:["$","$L24",null,{"gtmId":"GTM-N55KJQ5L"}]
14:["$","$1","c",{"children":[null,["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}]
15:["$","$1","c",{"children":[null,["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}]
16:["$","$1","c",{"children":[null,["$","$L2",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L3",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}]
17:["$","$1","c",{"children":["$L25",null,["$","$L26",null,{"children":["$","$27",null,{"name":"Next.MetadataOutlet","children":"$@28"}]}]]}]
29:[]
18:"$W29"
19:["$","$1","h",{"children":[null,["$","$L2a",null,{"children":"$L2b"}],["$","div",null,{"hidden":true,"children":["$","$L2c",null,{"children":["$","$27",null,{"name":"Next.Metadata","children":"$L2d"}]}]}],["$","meta",null,{"name":"next-size-adjust","content":""}]]}]
1d:["$","$L6",null,{"href":"/pricing","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Pricing"}]
1e:["$","li","Help",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/help","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Help"}]}]
1f:["$","li","API",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"https://docs.activecalculator.com/api-reference","target":"_blank","rel":"noopener noreferrer","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"API"}]}]
20:["$","li","Embed SDK JS",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"https://docs.activecalculator.com/sdks/embed-sdk/overview","target":"_blank","rel":"noopener noreferrer","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Embed SDK JS"}]}]
21:["$","div","Resources",{"children":[["$","h3",null,{"children":"Resources"}],["$","ul",null,{"role":"list","className":"mt-2 flex flex-col gap-2","children":[["$","li","Terms",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/terms","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Terms"}]}],["$","li","Privacy",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/privacy","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Privacy"}]}],["$","li","Book a Call",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/demo","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Book a Call"}]}],["$","li","Contact",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"/contact","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Contact"}]}],["$","li","Selvo",{"className":"text-mist-700 dark:text-mist-400","children":["$","$L6",null,{"href":"https://selvo.co","target":"_blank","rel":"noopener noreferrer","className":"transition-colors hover:text-mist-950 dark:hover:text-white","children":"Selvo"}]}]]}],"$undefined"]}]
2b:[["$","meta","0",{"charSet":"utf-8"}],["$","meta","1",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["$","meta","2",{"name":"theme-color","content":"#fff"}]]
2e:T42d,{"@context":"https://schema.org","@type":"Article","name":"LCD Calculator - Find the Least Common Denominator Instantly","dateModified":"2026-02-12T17:07:00.929Z","description":"Free LCD calculator to find the least common denominator of fractions instantly. Supports multiple fractions and mixed numbers.","author":{"name":"ActiveCalculator","@type":"Organization"},"datePublished":"2026-01-30T18:23:00.316Z","headline":"LCD Calculator - Find the Least Common Denominator Instantly","image":"https://activecalculator.com/api/og/calculator?title=LCD%20Calculator%20-%20Find%20the%20Least%20Common%20Denominator%20Instantly","mainEntityOfPage":{"@id":"https://activecalculator.com/calculators/math/lcd-calculator","@type":"WebPage"},"publisher":{"name":"ActiveCalculator","@type":"Organization","logo":{"@type":"ImageObject","height":112,"url":"https://activecalculator.com/logo.png","width":112}},"keywords":"LCD Calculator - Find the Least Common Denominator Instantly, tool, Math, Math calculator","url":"https://activecalculator.com/calculators/math/lcd-calculator"}2f:Te84,{"@type":"FAQPage","mainEntity":[{"name":"What is the least common denominator (LCD)?","@type":"Question","acceptedAnswer":{"@type":"Answer","text":"The LCD is the smallest positive number that all denominators in a set of fractions can divide into evenly. For 1/4 and 1/3, the LCD is 12 because both 4 and 3 divide evenly into 12, and no smaller number works for both. Finding the LCD lets you rewrite fractions so they have matching denominators."}},{"name":"What's the difference between LCD and LCM?","@type":"Question","acceptedAnswer":{"@type":"Answer","text":"They're the same calculation in different contexts. LCM (Least Common Multiple) is the general term for the smallest shared multiple of any numbers. LCD (Least Common Denominator) specifically refers to finding that value for fraction denominators. The LCD of 1/4 and 1/6 equals the LCM of 4 and 6—both are 12."}},{"name":"How do I find the LCD of two fractions?","@type":"Question","acceptedAnswer":{"@type":"Answer","text":"The quickest method: list multiples of each denominator until you find a match. For 1/6 and 1/8, multiples of 6 are 6, 12, 18, 24... and multiples of 8 are 8, 16, 24... The first number in both lists is 24, so that's your LCD."}},{"name":"Can I find the LCD of more than two fractions?","@type":"Question","acceptedAnswer":{"@type":"Answer","text":"Absolutely. The process is the same—find the smallest number all denominators divide into. For three or more fractions, prime factorization often saves time. Or just use this calculator, which handles any number of fractions."}},{"name":"Why do I need a common denominator to add fractions?","@type":"Question","acceptedAnswer":{"@type":"Answer","text":"The denominator tells you what size pieces you're working with. 1/4 means one piece when something is cut into 4 equal parts. 1/6 means one piece when cut into 6 parts. Those pieces are different sizes, so you can't add them directly. Converting to a common denominator puts everything in the same-sized pieces."}},{"name":"How do I find the LCD with mixed numbers?","@type":"Question","acceptedAnswer":{"@type":"Answer","text":"Only the fractional parts matter for finding the LCD. For 2 1/4 and 3 2/5, focus on 1/4 and 2/5. The LCD of denominators 4 and 5 is 20. The whole numbers (2 and 3) don't affect the LCD calculation."}},{"name":"What if the denominators have no common factors?","@type":"Question","acceptedAnswer":{"@type":"Answer","text":"When denominators share no factors (like 3 and 7), the LCD is simply their product. The LCD of 1/3 and 1/7 is 21. This is actually the easiest case—no prime factorization needed."}},{"name":"Is LCD the same as lowest common denominator?","@type":"Question","acceptedAnswer":{"@type":"Answer","text":"Yes, they're identical. \"Least common denominator\" and \"lowest common denominator\" both mean the smallest shared denominator. Different textbooks prefer different terms, but they describe exactly the same thing."}},{"name":"How do I use the LCD to add fractions?","@type":"Question","acceptedAnswer":{"@type":"Answer","text":"Once you have the LCD, convert each fraction: multiply both numerator and denominator by whatever makes the denominator equal the LCD. For 1/4 + 1/6 with LCD 12: 1/4 × 3/3 = 3/12, and 1/6 × 2/2 = 2/12. Then add the numerators: 3/12 + 2/12 = 5/12."}},{"name":"Can the LCD ever be smaller than one of the original denominators?","@type":"Question","acceptedAnswer":{"@type":"Answer","text":"Never. The LCD must be divisible by every denominator, so it's always at least as large as the biggest one. Sometimes the LCD equals the largest denominator (like when finding the LCD of 4 and 8, which is 8), but it can never be smaller."}}]}25:[["$","script",null,{"dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"name\":\"Home\",\"@type\":\"ListItem\",\"item\":\"https://activecalculator.com\",\"position\":1},{\"name\":\"Calculators\",\"@type\":\"ListItem\",\"item\":\"https://activecalculator.com/calculators\",\"position\":2},{\"name\":\"Math\",\"@type\":\"ListItem\",\"item\":\"https://activecalculator.com/calculators/math\",\"position\":3},{\"name\":\"LCD Calculator - Find the Least Common Denominator Instantly\",\"@type\":\"ListItem\",\"item\":\"https://activecalculator.com/calculators/math/lcd-calculator\",\"position\":4}]}"},"type":"application/ld+json"}],["$","script",null,{"dangerouslySetInnerHTML":{"__html":"$2e"},"type":"application/ld+json"}],["$","script",null,{"dangerouslySetInnerHTML":{"__html":"$2f"},"type":"application/ld+json"}],"$L30"]
31:I[65569,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","6956","static/chunks/66a6e935-aee5d3cb85c323ac.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","9858","static/chunks/9858-f1918ded0530ca69.js","609","static/chunks/609-95e41ae6a69b88b2.js","2456","static/chunks/2456-94cb89c116d69dd0.js","994","static/chunks/994-2c56ebb2d663b523.js","6472","static/chunks/6472-2ee935ddbae5821a.js","3349","static/chunks/app/(frontend)/calculators/%5Bcategory%5D/%5Bslug%5D/page-70bb6ad84377852d.js"],"JumplistProvider"]
32:I[52456,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","6956","static/chunks/66a6e935-aee5d3cb85c323ac.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","9858","static/chunks/9858-f1918ded0530ca69.js","609","static/chunks/609-95e41ae6a69b88b2.js","2456","static/chunks/2456-94cb89c116d69dd0.js","994","static/chunks/994-2c56ebb2d663b523.js","6472","static/chunks/6472-2ee935ddbae5821a.js","3349","static/chunks/app/(frontend)/calculators/%5Bcategory%5D/%5Bslug%5D/page-70bb6ad84377852d.js"],"RichText"]
33:I[52924,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","6956","static/chunks/66a6e935-aee5d3cb85c323ac.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","9858","static/chunks/9858-f1918ded0530ca69.js","609","static/chunks/609-95e41ae6a69b88b2.js","2456","static/chunks/2456-94cb89c116d69dd0.js","994","static/chunks/994-2c56ebb2d663b523.js","6472","static/chunks/6472-2ee935ddbae5821a.js","3349","static/chunks/app/(frontend)/calculators/%5Bcategory%5D/%5Bslug%5D/page-70bb6ad84377852d.js"],"ShareButtons"]
34:I[56472,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","6956","static/chunks/66a6e935-aee5d3cb85c323ac.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","9858","static/chunks/9858-f1918ded0530ca69.js","609","static/chunks/609-95e41ae6a69b88b2.js","2456","static/chunks/2456-94cb89c116d69dd0.js","994","static/chunks/994-2c56ebb2d663b523.js","6472","static/chunks/6472-2ee935ddbae5821a.js","3349","static/chunks/app/(frontend)/calculators/%5Bcategory%5D/%5Bslug%5D/page-70bb6ad84377852d.js"],"RenderBlocks"]
37:I[62540,[],"IconMark"]
30:["$","div",null,{"className":"min-h-screen bg-white","children":["$","$L31",null,{"children":["$","div",null,{"className":"py-10 lg:py-12 container","children":[["$","div",null,{"className":"mb-6","children":["$","div",null,{"className":"flex items-center flex-wrap gap-1 text-mist-600","children":[["$","$L6",null,{"className":"typo-small font-medium hover:text-blue-600 transition-colors duration-200","href":"/calculators","children":"Calculators"}],["$","svg",null,{"className":"text-mist-600","fill":"none","height":"16","stroke":"currentColor","strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":"2","viewBox":"0 0 24 24","width":"16","xmlns":"http://www.w3.org/2000/svg","children":["$","polyline",null,{"points":"9 18 15 12 9 6"}]}],["$","$L6",null,{"className":"typo-small font-medium hover:text-blue-600 transition-colors duration-200","href":"/calculators/math","children":"Math"}]]}]}],["$","div",null,{"className":"mb-8","children":[["$","h1",null,{"className":"typo-title mb-4 text-mist-950","children":"LCD Calculator - Find the Least Common Denominator Instantly"}],["$","div",null,{"className":"text-mist-600 typo-normal max-w-2xl mb-4","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Find the least common denominator of two or more fractions instantly. Supports simple fractions and mixed numbers with step-by-step guidance.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}],["$","div",null,{"className":"flex mt-4","children":["$","$L33",null,{"variant":"full","title":"LCD Calculator - Find the Least Common Denominator Instantly"}]}]]}],false,["$","div",null,{"className":"grid grid-cols-1 lg:grid-cols-6 gap-8","children":[["$","div",null,{"className":"lg:col-span-4","children":[["$","div",null,{"className":"bg-white rounded-lg shadow-sm p-8 mb-6","children":["$","$L34",null,{"blocks":[{"blockType":"blogContent","blogContentFields":{"settings":{"background":"default","paddingTop":"medium","paddingBottom":"medium"},"richText":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Fractions with different denominators can feel like trying to compare apples and oranges. This LCD calculator takes the guesswork out of finding the least common denominator, giving you the answer instantly so you can get back to solving the actual problem.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Whether you're helping your child with tonight's math homework, brushing up on skills you haven't used since school, or working through a recipe that calls for 1/3 cup of this and 1/4 cup of that, this tool finds the smallest common denominator for any set of fractions. Just enter your numbers, and you'll have your answer in seconds.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"What is the Least Common Denominator?","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h2"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The least common denominator (LCD) is the smallest number that all your denominators can divide into evenly. If that sounds abstract, here's a simpler way to think about it: the LCD is the smallest \"meeting point\" where different fractions can be compared or combined.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Here's why that matters in practice. Say you want to add 1/4 and 1/6. You can't just add the tops and bottoms together—that's a common mistake that gives you the wrong answer. Instead, you need both fractions to have the same denominator first.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The LCD of 4 and 6 is 12. Once you know that, the conversion is straightforward:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/4 becomes 3/12 (multiply top and bottom by 3)","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/6 becomes 2/12 (multiply top and bottom by 2)","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Now you can add them: 3/12 + 2/12 = 5/12","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":3}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The LCD makes this work because 12 is the smallest number that both 4 and 6 divide into cleanly. You could use 24 or 48 as a common denominator too, but then you'd need to simplify at the end. Using the LCD keeps your numbers manageable.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"LCD vs. LCM: Clearing Up the Confusion","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h2"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"If you've seen both \"LCD\" and \"LCM\" and wondered whether they're the same thing, you're not alone. Here's the quick answer: ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"when you're finding the LCD of fractions, you're finding the LCM of the denominators","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":". Same math, different context.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"type":"table","children":[{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"Term","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":1,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"What It Means","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":1,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"When You Use It","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":1,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1},{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"LCM","format":1,"style":"","detail":0,"mode":"normal","version":1},{"type":"text","text":" (Least Common Multiple)","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"Smallest number that's a multiple of all given numbers","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"General math problems","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1},{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"LCD","format":1,"style":"","detail":0,"mode":"normal","version":1},{"type":"text","text":" (Least Common Denominator)","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"Smallest shared denominator for a set of fractions","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"Fraction operations","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1}],"direction":"ltr","format":"","indent":0,"version":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"So the LCM of 4 and 6 is 12. And the LCD of 1/4 and 1/6 is also 12. You're doing the same calculation—LCD just tells you that you're specifically working with fraction denominators.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"How to Find LCD by Hand","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h2"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Knowing how to find the LCD manually is genuinely useful. It helps you estimate answers quickly, catch calculator mistakes, and—let's be honest—pass tests where calculators aren't allowed. There are two solid methods, and the best one depends on your numbers.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Method 1: List the Multiples","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h3"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"This is the most intuitive approach and works great for smaller numbers.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Steps:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Write out multiples of each denominator","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Find the smallest number that shows up in every list","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"number","start":1,"tag":"ol"},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Example: LCD of 1/4 and 1/6","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Multiples of 4: 4, 8, ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"12","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":", 16, 20, 24...","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Multiples of 6: 6, ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"12","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":", 18, 24, 30...","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Both lists contain 12, and it's the smallest shared number. ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"LCD = 12","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"This method is quick when you can spot the common multiple within the first several terms. For larger or \"unfriendly\" numbers, the next method works better.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Method 2: Prime Factorization","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h3"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"This approach handles bigger numbers without endless listing.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Steps:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Break each denominator into prime factors","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"For each prime, take the highest power that appears","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Multiply those together","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":3}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"number","start":1,"tag":"ol"},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Example: LCD of 5/12 and 7/18","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"First, find the prime factors:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"12 = 2 × 2 × 3 = 2² × 3","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"18 = 2 × 3 × 3 = 2 × 3²","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Now take the highest power of each prime:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Highest power of 2: 2² = 4","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Highest power of 3: 3² = 9","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Multiply: 4 × 9 = ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"36","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Both methods give you 36. Prime factorization just gets you there faster when listing multiples would take forever.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Quick Reference: Common LCD Pairs","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h2"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Some LCD combinations come up again and again. Having these memorized saves time:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"type":"table","children":[{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"Denominators","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":1,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"LCD","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":1,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"Why","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":1,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1},{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"2 and 3","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"6","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"2 × 3 (no shared factors)","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1},{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"3 and 4","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"12","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"3 × 4 (no shared factors)","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1},{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"4 and 6","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"12","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"Both divide into 12","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1},{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"3 and 5","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"15","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"3 × 5 (no shared factors)","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1},{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"5 and 6","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"30","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"5 × 6 (no shared factors)","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1},{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"6 and 8","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"24","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"Both share factor of 2","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1},{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"4 and 10","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"20","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"Both share factor of 2","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1},{"type":"tablerow","children":[{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"8 and 12","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"24","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1},{"type":"tablecell","children":[{"type":"paragraph","children":[{"type":"text","text":"Both share factor of 4","format":0,"style":"","detail":0,"mode":"normal","version":1}],"direction":"ltr","format":"","indent":0,"textFormat":0,"textStyle":"","version":1}],"direction":"ltr","format":"","indent":0,"version":1,"backgroundColor":null,"colSpan":1,"headerState":0,"rowSpan":1}],"direction":"ltr","format":"","indent":0,"version":1}],"direction":"ltr","format":"","indent":0,"version":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Notice the pattern: when denominators share no common factors, just multiply them. When they do share factors, the LCD is smaller than their product.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"How to Use This Calculator","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h2"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Finding your LCD takes just a few seconds:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Pick your fraction type.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" Choose \"Simple fraction\" for regular fractions like 2/5, or \"Mixed number\" for values like 3 1/2.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Enter your first fraction.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" Type the numerator (top number) and denominator (bottom number).","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Add more fractions.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" Click \"Add another\" for each additional fraction. There's no limit—add as many as your problem requires.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":3},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Read your result.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" The LCD appears instantly below your fractions and updates automatically as you type.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":4},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Make changes anytime.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" Use \"Remove\" to delete a fraction, or simply edit the numbers to try different combinations.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":5}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"number","start":1,"tag":"ol"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"That's it. No buttons to click, no waiting—just type and get your answer.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Practical Examples","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h2"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Abstract math makes more sense with real scenarios. Here's how LCD shows up in everyday situations.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Example 1: Combining Recipe Ingredients","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h3"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"You're making salad dressing that calls for 1/4 cup olive oil and 1/3 cup vinegar. You want to know the total liquid amount.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Finding the LCD:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Denominators: 4 and 3","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"These share no common factors, so LCD = 4 × 3 = ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"12","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Converting and adding:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/4 = 3/12","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/3 = 4/12","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Total: 7/12 cup of liquid","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":3}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Example 2: Splitting Your Day","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h3"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"You spend 1/2 of your workday in meetings, 1/3 on focused work, and 1/6 on email. Does that actually add up?","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Finding the LCD:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Denominators: 2, 3, and 6","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"6 is already a multiple of both 2 and 3, so ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"LCD = 6","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Converting and adding:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/2 = 3/6","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/3 = 2/6","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/6 = 1/6","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":3},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Total: 6/6 = 1 whole day ✓","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":4}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The fractions check out—your entire day is accounted for.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Example 3: Comparing Measurements","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h3"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"You're at the hardware store choosing between two boards. One is 3/8 inch thick, the other is 5/16 inch. Which is thicker?","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Finding the LCD:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Denominators: 8 and 16","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"16 is a multiple of 8, so ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"LCD = 16","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Converting to compare:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"3/8 = 6/16","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"5/16 = 5/16","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Now it's clear: 6/16 > 5/16, so the 3/8 inch board is thicker.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Example 4: Three Unrelated Denominators","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h3"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Your study schedule allocates 1/2 hour to math, 1/3 hour to reading, and 1/5 hour to vocabulary. What's the total study time?","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Finding the LCD:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Denominators: 2, 3, and 5","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"No shared factors, so LCD = 2 × 3 × 5 = ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"30","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Converting and adding:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/2 = 15/30","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/3 = 10/30","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/5 = 6/30","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":3},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Total: 31/30 = 1 1/30 hours (just over an hour)","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":4}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Example 5: Mixed Numbers","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h3"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"A recipe needs 2 1/4 cups of flour and 1 2/3 cups of sugar. What's the combined amount?","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Finding the LCD (focus on the fractional parts):","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Denominators: 4 and 3","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"LCD = ","type":"text","version":1},{"detail":0,"format":1,"mode":"normal","style":"","text":"12","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Converting the fractions:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"1/4 = 3/12","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"2/3 = 8/12","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":2}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Adding the mixed numbers:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"2 3/12 + 1 8/12 = 3 11/12 cups total","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"listitem","version":1,"value":1}],"direction":null,"format":"","indent":0,"type":"list","version":1,"listType":"bullet","start":1,"tag":"ul"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Common Mistakes to Avoid","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h2"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Even with the right LCD, a few pitfalls can trip you up:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Forgetting to adjust the numerator.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" When you multiply the denominator to reach the LCD, you must multiply the numerator by the same amount. If 1/4 becomes ?/12, multiply both top and bottom by 3 to get 3/12—not 1/12.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Using any common denominator instead of the least.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" Technically, 24 works as a common denominator for 4 and 6. But using the LCD (12) keeps your numbers smaller and often lets you skip simplifying at the end.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Adding denominators together.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" A classic error: thinking 1/4 + 1/6 = 2/10. It doesn't work that way. The denominator represents the size of each piece, and you can't add pieces of different sizes directly.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Assuming the LCD is always the product.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" The LCD of 4 and 6 isn't 24 (their product)—it's 12. When denominators share factors, the LCD is smaller than their product.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"When Do You Actually Need the LCD?","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h2"},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The LCD comes up more often than you might expect:","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Adding and subtracting fractions","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" — This is the most common use. Any time you combine fractions with different denominators, you need the LCD first.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Comparing fractions","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" — Is 5/8 larger than 7/12? Convert both to the LCD (24), and you get 15/24 vs. 14/24. Now it's obvious that 5/8 is larger.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Solving equations","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" — Many algebra problems involve adding fractions with variables. Finding the LCD is often the key first step.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Real-world calculations","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" — Cooking, construction, time management, finances—fractions appear constantly. The LCD helps you combine and compare them accurately.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Tips for Working with Fractions","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"heading","version":1,"tag":"h2"},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Look for one denominator being a multiple of the other.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" If you're working with 1/4 and 3/8, notice that 8 is a multiple of 4. That makes 8 your LCD automatically—no calculation needed.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"When denominators share no factors, just multiply.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" The LCD of 2/5 and 3/7 is 35 (5 × 7). When there's no common factor, the product is always the LCD.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Simplify at the end, not before.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" Find your LCD, do your calculation, then reduce if possible. Trying to simplify too early often creates more work.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Use this calculator to double-check your work.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" There's no shame in verifying. Even experienced math teachers occasionally make arithmetic errors. A quick check catches mistakes before they matter.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""},{"children":[{"detail":0,"format":1,"mode":"normal","style":"","text":"Recognize that it gets easier.","type":"text","version":1},{"detail":0,"format":0,"mode":"normal","style":"","text":" If fractions feel frustrating right now, that's normal. The more you practice finding common denominators, the more patterns you'll recognize. Soon you'll spot that the LCD of 6 and 9 is 18 without even thinking about it.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}},"id":"697cf70475d53b0004a62638"}]}]}],"$L35"]}],"$L36"]}]]}]}]}]
28:null
2d:[["$","title","0",{"children":"LCD Calculator - Find the Least Common Denominator Instantly"}],["$","meta","1",{"name":"description","content":"Free LCD calculator to find the least common denominator of fractions instantly. Supports multiple fractions and mixed numbers."}],["$","link","2",{"rel":"canonical","href":"https://activecalculator.com/calculators/math/lcd-calculator"}],["$","meta","3",{"property":"og:title","content":"LCD Calculator - Find the Least Common Denominator Instantly"}],["$","meta","4",{"property":"og:description","content":"Free LCD calculator to find the least common denominator of fractions instantly. Supports multiple fractions and mixed numbers."}],["$","meta","5",{"property":"og:url","content":"https://activecalculator.com/calculators/math/lcd-calculator"}],["$","meta","6",{"property":"og:site_name","content":"ActiveCalculator"}],["$","meta","7",{"property":"og:locale","content":"en_US"}],["$","meta","8",{"property":"og:image","content":"https://activecalculator.com/api/og/calculator?title=LCD%20Calculator%20-%20Find%20the%20Least%20Common%20Denominator%20Instantly"}],["$","meta","9",{"property":"og:image:width","content":"1200"}],["$","meta","10",{"property":"og:image:height","content":"630"}],["$","meta","11",{"property":"og:image:alt","content":"LCD Calculator - Find the Least Common Denominator Instantly"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"@activecalculator"}],["$","meta","15",{"name":"twitter:creator","content":"@activecalculator"}],["$","meta","16",{"name":"twitter:title","content":"LCD Calculator - Find the Least Common Denominator Instantly"}],["$","meta","17",{"name":"twitter:description","content":"Free LCD calculator to find the least common denominator of fractions instantly. Supports multiple fractions and mixed numbers."}],["$","meta","18",{"name":"twitter:image","content":"https://activecalculator.com/api/og/calculator?title=LCD%20Calculator%20-%20Find%20the%20Least%20Common%20Denominator%20Instantly"}],["$","link","19",{"rel":"icon","href":"/favicon.ico?756f06c5b2066fec","type":"image/x-icon","sizes":"48x48"}],["$","$L37","20",{}]]
3d:I[51318,["9310","static/chunks/f8d55a4d-f82e876c81147bfd.js","6956","static/chunks/66a6e935-aee5d3cb85c323ac.js","7821","static/chunks/7821-fecf606f47f1f58d.js","8963","static/chunks/8963-69c253eec8d741c5.js","9858","static/chunks/9858-f1918ded0530ca69.js","609","static/chunks/609-95e41ae6a69b88b2.js","2456","static/chunks/2456-94cb89c116d69dd0.js","994","static/chunks/994-2c56ebb2d663b523.js","6472","static/chunks/6472-2ee935ddbae5821a.js","3349","static/chunks/app/(frontend)/calculators/%5Bcategory%5D/%5Bslug%5D/page-70bb6ad84377852d.js"],"Calculator"]
35:["$","div",null,{"className":"bg-white rounded-lg shadow-sm p-8","children":[["$","h2",null,{"className":"typo-large mb-6 text-mist-950","children":"Frequently Asked Questions"}],["$","div",null,{"className":"space-y-6","children":[["$","div","0",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"What is the least common denominator (LCD)?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The LCD is the smallest positive number that all denominators in a set of fractions can divide into evenly. For 1/4 and 1/3, the LCD is 12 because both 4 and 3 divide evenly into 12, and no smaller number works for both. Finding the LCD lets you rewrite fractions so they have matching denominators.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}],["$","div","1",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"What's the difference between LCD and LCM?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"They're the same calculation in different contexts. LCM (Least Common Multiple) is the general term for the smallest shared multiple of any numbers. LCD (Least Common Denominator) specifically refers to finding that value for fraction denominators. The LCD of 1/4 and 1/6 equals the LCM of 4 and 6—both are 12.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}],["$","div","2",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"How do I find the LCD of two fractions?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The quickest method: list multiples of each denominator until you find a match. For 1/6 and 1/8, multiples of 6 are 6, 12, 18, 24... and multiples of 8 are 8, 16, 24... The first number in both lists is 24, so that's your LCD.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}],["$","div","3",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"Can I find the LCD of more than two fractions?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Absolutely. The process is the same—find the smallest number all denominators divide into. For three or more fractions, prime factorization often saves time. Or just use this calculator, which handles any number of fractions.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}],["$","div","4",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"Why do I need a common denominator to add fractions?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"The denominator tells you what size pieces you're working with. 1/4 means one piece when something is cut into 4 equal parts. 1/6 means one piece when cut into 6 parts. Those pieces are different sizes, so you can't add them directly. Converting to a common denominator puts everything in the same-sized pieces.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}],"$L38","$L39","$L3a","$L3b","$L3c"]}]]}]
36:["$","div",null,{"className":"lg:col-span-2","children":[["$","div",null,{"className":"sticky top-24 mb-6 max-h-[calc(100vh-6rem)] overflow-y-auto space-y-4","children":[["$","$L3d",null,{"className":"rounded-xl shadow-sm","id":"cmfcfwbor0000gy041cc4aguq"}],["$","div",null,{"className":"bg-white rounded-lg shadow-sm p-4","children":["$","nav",null,{"aria-label":"Table of contents","children":[["$","h2",null,{"className":"text-lg font-display font-normal mb-4 text-mist-900","children":"Table of Contents"}],["$","ul",null,{"className":"space-y-2.5","children":[["$","li","what-is-the-least-common-denominator",{"className":"","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#what-is-the-least-common-denominator","children":"What is the Least Common Denominator?"}]}],["$","li","lcd-vs-lcm-clearing-up-the-confusion",{"className":"","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#lcd-vs-lcm-clearing-up-the-confusion","children":"LCD vs. LCM: Clearing Up the Confusion"}]}],["$","li","how-to-find-lcd-by-hand",{"className":"","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#how-to-find-lcd-by-hand","children":"How to Find LCD by Hand"}]}],["$","li","method-1-list-the-multiples",{"className":"ml-3","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#method-1-list-the-multiples","children":"Method 1: List the Multiples"}]}],["$","li","method-2-prime-factorization",{"className":"ml-3","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#method-2-prime-factorization","children":"Method 2: Prime Factorization"}]}],["$","li","quick-reference-common-lcd-pairs",{"className":"","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#quick-reference-common-lcd-pairs","children":"Quick Reference: Common LCD Pairs"}]}],["$","li","how-to-use-this-calculator",{"className":"","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#how-to-use-this-calculator","children":"How to Use This Calculator"}]}],["$","li","practical-examples",{"className":"","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#practical-examples","children":"Practical Examples"}]}],["$","li","example-1-combining-recipe-ingredients",{"className":"ml-3","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#example-1-combining-recipe-ingredients","children":"Example 1: Combining Recipe Ingredients"}]}],["$","li","example-2-splitting-your-day",{"className":"ml-3","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#example-2-splitting-your-day","children":"Example 2: Splitting Your Day"}]}],["$","li","example-3-comparing-measurements",{"className":"ml-3","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#example-3-comparing-measurements","children":"Example 3: Comparing Measurements"}]}],"$L3e","$L3f","$L40","$L41","$L42"]}]]}]}]]}],"$L43"]}]
38:["$","div","5",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"How do I find the LCD with mixed numbers?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Only the fractional parts matter for finding the LCD. For 2 1/4 and 3 2/5, focus on 1/4 and 2/5. The LCD of denominators 4 and 5 is 20. The whole numbers (2 and 3) don't affect the LCD calculation.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}]
39:["$","div","6",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"What if the denominators have no common factors?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"When denominators share no factors (like 3 and 7), the LCD is simply their product. The LCD of 1/3 and 1/7 is 21. This is actually the easiest case—no prime factorization needed.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}]
3a:["$","div","7",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"Is LCD the same as lowest common denominator?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Yes, they're identical. \"Least common denominator\" and \"lowest common denominator\" both mean the smallest shared denominator. Different textbooks prefer different terms, but they describe exactly the same thing.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}]
3b:["$","div","8",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"How do I use the LCD to add fractions?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Once you have the LCD, convert each fraction: multiply both numerator and denominator by whatever makes the denominator equal the LCD. For 1/4 + 1/6 with LCD 12: 1/4 × 3/3 = 3/12, and 1/6 × 2/2 = 2/12. Then add the numerators: 3/12 + 2/12 = 5/12.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}]
3c:["$","div","9",{"className":"pb-6 last:pb-0","children":[["$","h3",null,{"className":"text-lg font-medium text-mist-950 mb-3","children":"Can the LCD ever be smaller than one of the original denominators?"}],["$","div",null,{"className":"prose max-w-none text-mist-600","children":["$","$L32",null,{"content":{"root":{"children":[{"children":[{"detail":0,"format":0,"mode":"normal","style":"","text":"Never. The LCD must be divisible by every denominator, so it's always at least as large as the biggest one. Sometimes the LCD equals the largest denominator (like when finding the LCD of 4 and 8, which is 8), but it can never be smaller.","type":"text","version":1}],"direction":null,"format":"","indent":0,"type":"paragraph","version":1,"textFormat":0,"textStyle":""}],"direction":null,"format":"","indent":0,"type":"root","version":1}}}]}]]}]
3e:["$","li","example-4-three-unrelated-denominators",{"className":"ml-3","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#example-4-three-unrelated-denominators","children":"Example 4: Three Unrelated Denominators"}]}]
3f:["$","li","example-5-mixed-numbers",{"className":"ml-3","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#example-5-mixed-numbers","children":"Example 5: Mixed Numbers"}]}]
40:["$","li","common-mistakes-to-avoid",{"className":"","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#common-mistakes-to-avoid","children":"Common Mistakes to Avoid"}]}]
41:["$","li","when-do-you-actually-need-the-lcd",{"className":"","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#when-do-you-actually-need-the-lcd","children":"When Do You Actually Need the LCD?"}]}]
42:["$","li","tips-for-working-with-fractions",{"className":"","children":["$","$L6",null,{"className":"block py-1 text-mist-600 hover:text-mist-900 hover:underline transition-colors leading-relaxed text-sm no-underline","href":"#tips-for-working-with-fractions","children":"Tips for Working with Fractions"}]}]
43:["$","div",null,{"className":"space-y-6","children":false}]