{"id":809,"date":"2025-10-15T11:09:49","date_gmt":"2025-10-15T11:09:49","guid":{"rendered":"https:\/\/kapdec.com\/help\/?post_type=docs&#038;p=809"},"modified":"2026-04-10T10:38:35","modified_gmt":"2026-04-10T10:38:35","slug":"what-is-lcm","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/what-is-lcm\/","title":{"rendered":"What is LCM(Least Common Multiple)?"},"content":{"rendered":"<p><b>Least Common Multiple\u00a0(L.C.M.)<\/b><\/p>\n<p>The multiples which are common to a given set of numbers are called their\u00a0<b>common multiples.<\/b><\/p>\n<p>For example, the common multiples of 6 and 8 are 24, 48, 72, 96 and so on.<\/p>\n<p>The lowest among these common multiples is 24 which is the Lowest Common Multiple of 6 and 8.<\/p>\n<p>Thus,\u00a0the multiple which is smallest among the common multiples of a given set of numbers is called their<b>\u00a0Lowest Common Multiple (L.C.M.).<\/b><\/p>\n<p><b>Example-<\/b>\u00a0Let us take 2 numbers 12 and 18 and find their LCM.<\/p>\n<p>Multiples of 12 = 12, 24,\u00a036, 48, 60,\u00a072, 84, 96,\u00a0108, &#8230;<\/p>\n<p>Multiples of 18 = 18,\u00a036, 54,\u00a072, 90,\u00a0108, 126, &#8230;<\/p>\n<p><b>Common\u00a0multiples<\/b>\u00a0of\u00a012\u00a0and\u00a018\u00a0are\u00a036, 72, 108 and so on.<\/p>\n<p>Smallest among all common\u00a0multiples\u00a0is\u00a036.<\/p>\n<p>Thus,\u00a0<b>L.C.M. of\u00a012\u00a0and\u00a018\u00a0=\u00a036<\/b><\/p>\n<ul>\n<li><b>LCM byPrime Factorization Method<\/b><\/li>\n<\/ul>\n<ul>\n<li>In this method, we express the given set of numbers as a product of their prime factors.<\/li>\n<\/ul>\n<ul>\n<li>The LCM of the twonumbers is\u00a0calculated as\u00a0the product of the prime factors counted the maximum numberof times they occur in any of the numbers.<\/li>\n<\/ul>\n<p><b>Example-\u00a0<\/b><\/p>\n<ol>\n<li>Find the\u00a0LCM\u00a0of 18 and 24.<\/li>\n<\/ol>\n<p>Let us find the prime factorization of 18 and 24.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-810\" src=\"https:\/\/kapdec.com\/help\/venture\/wp-content\/uploads\/2025\/10\/lcm.gif\" alt=\"\" width=\"24\" height=\"24\" \/><\/p>\n<p>So, 18 = 2 \u00d7 3 \u00d7 3<\/p>\n<p>24 = 2 \u00d7 2 \u00d7 2 \u00d7 3<\/p>\n<p>Maximum number of times prime factor 2 occurs among 18 and 24 is 3.<\/p>\n<p>Similarly, 3 occurs maximum of 2 times.<\/p>\n<p>LCM of 18 and 24 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3\u00a0 = 72<\/p>\n<p>Thus,\u00a0<b>LCM (18 and 24) = 72<\/b><\/p>\n<p><b>Relationship between\u00a0HCF and LCM<\/b><\/p>\n<p>The product of HCF and LCM of two numbers is equal to the product of the numbers.<\/p>\n<p>i.e.\u00a0<b>HCF \u00d7 LCM = Product of the Numbers<\/b><\/p>\n<p><b>Example-\u00a0<\/b>Given two numbers: 6 and 8<\/p>\n<p>HCF (6 and 8) = 2<\/p>\n<p>LCM (6 and 8) = 24<\/p>\n<p>Product (6 and 8) = 6 \u00d7 8 = 48<\/p>\n<p>Now, HCF \u00d7 LCM = 2 \u00d7 24 = 48<\/p>\n<p>Thus,\u00a0<b>HCF \u00d7 LCM = Product of the Numbers.<\/b><\/p>\n<p><b>Can you solve\u00a0this??<\/b><\/p>\n<p>#Find HCF and LCM of the form- 2222&#8230;.30 times and 3333&#8230;.70 times (any random numbers)<\/p>\n<p><b>Solution:<\/b><\/p>\n<p><b>HCF\u00a0<\/b><\/p>\n<ul>\n<li>Take HCF of no. that is being repeated&#8230;i.e. HCF of 2 &amp; 3.<br \/>\ni.e. 1<\/li>\n<li>Take HCF of no. of time these nos. are being repeated i.e. HCF of 30 and 70 is 10.<\/li>\n<\/ul>\n<ul>\n<li>So, the HCF of the two given numbers is 1&#8230;written 10 times.<\/li>\n<\/ul>\n<p><b>LCM\u00a0<\/b><\/p>\n<ul>\n<li>Take LCM of no. that is being repeated&#8230;i.e. LCM of 2 &amp; 3.<br \/>\ni.e. 6<\/li>\n<li>Take LCM of no. of time these nos. are being repeated i.e. LCM of 30 and 70 is 210.<\/li>\n<\/ul>\n<ul>\n<li>So, the LCM is 6&#8230;written 210 times<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Least Common Multiple\u00a0(L.C.M.) The multiples which are common to a given set of numbers are called their\u00a0common multiples. For example, the common multiples of 6 and 8 are 24, 48, 72, 96 and so on. The lowest among these common multiples is 24 which is the Lowest Common Multiple of 6 and 8. Thus,\u00a0the multiple [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[590],"tags":[595],"class_list":["post-809","post","type-post","status-publish","format-standard","hentry","category-grade-5","tag-grade-5-mathematics"],"_links":{"self":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/809","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/comments?post=809"}],"version-history":[{"count":2,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/809\/revisions"}],"predecessor-version":[{"id":1681,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/809\/revisions\/1681"}],"wp:attachment":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/media?parent=809"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/categories?post=809"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/tags?post=809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}