{"id":251109,"date":"2025-07-10T14:50:06","date_gmt":"2025-07-10T14:50:06","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=251109"},"modified":"2025-07-10T14:50:08","modified_gmt":"2025-07-10T14:50:08","slug":"find-the-lcm-of-the-list-of-numbers","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/10\/find-the-lcm-of-the-list-of-numbers\/","title":{"rendered":"Find the LCM of the list of numbers."},"content":{"rendered":"\n<p>Find the LCM of the list of numbers. 9 and 21 The LCM of 9 and 21 is<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the Least Common Multiple (LCM) of 9 and 21, we will follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Prime Factorization<\/h3>\n\n\n\n<p>We start by finding the prime factorization of each number.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Prime factorization of 9:<\/strong><br>9 = 3 \u00d7 3 = 3\u00b2<\/li>\n\n\n\n<li><strong>Prime factorization of 21:<\/strong><br>21 = 3 \u00d7 7<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Identify the Highest Powers of All Prime Factors<\/h3>\n\n\n\n<p>Now, we list the prime factors of both numbers and select the highest powers of each prime.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For the prime <strong>3<\/strong>, the highest power is <strong>3\u00b2<\/strong> (from 9).<\/li>\n\n\n\n<li>For the prime <strong>7<\/strong>, the highest power is <strong>7<\/strong> (from 21).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Multiply the Highest Powers<\/h3>\n\n\n\n<p>To find the LCM, we multiply these highest powers:LCM=32\u00d77=9\u00d77=63LCM = 3\u00b2 \u00d7 7 = 9 \u00d7 7 = 63LCM=32\u00d77=9\u00d77=63<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Verify the Result<\/h3>\n\n\n\n<p>To verify, we check if 63 is divisible by both 9 and 21:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>63 \u00f7 9 = 7 (an integer, so 63 is divisible by 9).<\/li>\n\n\n\n<li>63 \u00f7 21 = 3 (an integer, so 63 is divisible by 21).<\/li>\n<\/ul>\n\n\n\n<p>Since 63 is divisible by both 9 and 21, we confirm that it is indeed the LCM.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The LCM of 9 and 21 is <strong>63<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The LCM is the smallest number that both 9 and 21 divide into without leaving a remainder. We use the prime factorization method to find it. First, we find the prime factors of each number, then we take the highest powers of all primes involved. The LCM is the product of these highest powers. In this case, 3\u00b2 and 7 are the highest powers, giving us an LCM of 63. This is the smallest multiple of both 9 and 21.<\/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-banner9-31.jpeg\" alt=\"\" class=\"wp-image-251115\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the LCM of the list of numbers. 9 and 21 The LCM of 9 and 21 is The Correct Answer and Explanation is: To find the Least Common Multiple (LCM) of 9 and 21, we will follow these steps: Step 1: Prime Factorization We start by finding the prime factorization of each number. Step [&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-251109","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/251109","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=251109"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/251109\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=251109"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=251109"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=251109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}