{"id":240009,"date":"2025-07-03T06:41:04","date_gmt":"2025-07-03T06:41:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=240009"},"modified":"2025-07-03T06:41:06","modified_gmt":"2025-07-03T06:41:06","slug":"find-the-lcm-of-the-following-numbers-by-prime-factorization-method","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/find-the-lcm-of-the-following-numbers-by-prime-factorization-method\/","title":{"rendered":"Find the LCM of the following numbers by prime factorization method"},"content":{"rendered":"\n<p>Find the LCM of the following numbers by prime factorization method: 18 and 27.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the least common multiple (LCM) of 18 and 27 using the prime factorization method, we first need to express each number as a product of prime factors.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Prime Factorization of 18 and 27<\/h3>\n\n\n\n<p><strong>Prime factorization of 18:<\/strong><br>Start by dividing 18 by the smallest prime number (2).<br>18 \u00f7 2 = 9<\/p>\n\n\n\n<p>Now, factor 9:<br>9 \u00f7 3 = 3<br>3 \u00f7 3 = 1<\/p>\n\n\n\n<p>So, the prime factorization of 18 is:<br>18 = 2 \u00d7 3\u00b2<\/p>\n\n\n\n<p><strong>Prime factorization of 27:<\/strong><br>Start by dividing 27 by the smallest prime number (3).<br>27 \u00f7 3 = 9<br>9 \u00f7 3 = 3<br>3 \u00f7 3 = 1<\/p>\n\n\n\n<p>So, the prime factorization of 27 is:<br>27 = 3\u00b3<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Determine the LCM<\/h3>\n\n\n\n<p>To find the LCM, we take the highest powers of all prime factors present in both numbers. We compare the prime factorizations of 18 and 27:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The prime factors of 18 are 2 and 3\u00b2.<\/li>\n\n\n\n<li>The prime factor of 27 is 3\u00b3.<\/li>\n<\/ul>\n\n\n\n<p>Now, the LCM is obtained by taking the highest power of each prime factor:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The highest power of 2 is 2\u00b9 (since 2 only appears in 18).<\/li>\n\n\n\n<li>The highest power of 3 is 3\u00b3 (since 27 has 3\u00b3, which is higher than 3\u00b2).<\/li>\n<\/ul>\n\n\n\n<p>Thus, the LCM is:<br>LCM = 2\u00b9 \u00d7 3\u00b3 = 2 \u00d7 27 = 54<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Conclusion<\/h3>\n\n\n\n<p>The least common multiple of 18 and 27 is 54.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The prime factorization method involves breaking down each number into its prime factors and then taking the highest powers of each prime factor from both numbers. This ensures that the LCM is the smallest number that both 18 and 27 divide into without a remainder. In this case, 54 is the smallest such number.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-91.jpeg\" alt=\"\" class=\"wp-image-240010\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the LCM of the following numbers by prime factorization method: 18 and 27. The Correct Answer and Explanation is: To find the least common multiple (LCM) of 18 and 27 using the prime factorization method, we first need to express each number as a product of prime factors. Step 1: Prime Factorization of 18 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-240009","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240009","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=240009"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240009\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240009"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240009"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240009"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}