{"id":263910,"date":"2025-07-21T09:58:01","date_gmt":"2025-07-21T09:58:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=263910"},"modified":"2025-07-21T09:58:10","modified_gmt":"2025-07-21T09:58:10","slug":"find-the-greatest-common-factors-and-least-common-multiple-of-the-following-numbers","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/find-the-greatest-common-factors-and-least-common-multiple-of-the-following-numbers\/","title":{"rendered":"Find the Greatest Common Factors and Least Common Multiple of the following numbers"},"content":{"rendered":"\n<p> Find the Greatest Common Factors and Least Common Multiple of the following numbers: 1. 12, 24, 36 2.. 10, 25, 50 3. 38, 86, 120 4. 9, 36, 72 5. 66, 142, 168<\/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 <strong>Greatest Common Factor (GCF)<\/strong> and <strong>Least Common Multiple (LCM)<\/strong> of the given numbers, we can follow these steps:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">1. GCF and LCM of 12, 24, 36<\/h3>\n\n\n\n<p><strong>Step 1: Prime Factorization<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>12 = 2\u00b2 \u00d7 3<\/li>\n\n\n\n<li>24 = 2\u00b3 \u00d7 3<\/li>\n\n\n\n<li>36 = 2\u00b2 \u00d7 3\u00b2<\/li>\n<\/ul>\n\n\n\n<p><strong>GCF<\/strong>: The GCF is obtained by taking the lowest powers of all the prime factors that appear in all factorizations.<br>GCF = 2\u00b2 \u00d7 3 = 12.<\/p>\n\n\n\n<p><strong>LCM<\/strong>: The LCM is obtained by taking the highest powers of all prime factors.<br>LCM = 2\u00b3 \u00d7 3\u00b2 = 72.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2. GCF and LCM of 10, 25, 50<\/h3>\n\n\n\n<p><strong>Step 1: Prime Factorization<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>10 = 2 \u00d7 5<\/li>\n\n\n\n<li>25 = 5\u00b2<\/li>\n\n\n\n<li>50 = 2 \u00d7 5\u00b2<\/li>\n<\/ul>\n\n\n\n<p><strong>GCF<\/strong>: The GCF is the product of the lowest powers of common prime factors.<br>GCF = 5.<\/p>\n\n\n\n<p><strong>LCM<\/strong>: The LCM is the product of the highest powers of all prime factors.<br>LCM = 2 \u00d7 5\u00b2 = 50.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">3. GCF and LCM of 38, 86, 120<\/h3>\n\n\n\n<p><strong>Step 1: Prime Factorization<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>38 = 2 \u00d7 19<\/li>\n\n\n\n<li>86 = 2 \u00d7 43<\/li>\n\n\n\n<li>120 = 2\u00b3 \u00d7 3 \u00d7 5<\/li>\n<\/ul>\n\n\n\n<p><strong>GCF<\/strong>: The GCF is the product of the lowest powers of common prime factors.<br>GCF = 2.<\/p>\n\n\n\n<p><strong>LCM<\/strong>: The LCM is the product of the highest powers of all prime factors.<br>LCM = 2\u00b3 \u00d7 3 \u00d7 5 \u00d7 19 \u00d7 43 = 2,5920.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">4. GCF and LCM of 9, 36, 72<\/h3>\n\n\n\n<p><strong>Step 1: Prime Factorization<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>9 = 3\u00b2<\/li>\n\n\n\n<li>36 = 2\u00b2 \u00d7 3\u00b2<\/li>\n\n\n\n<li>72 = 2\u00b3 \u00d7 3\u00b2<\/li>\n<\/ul>\n\n\n\n<p><strong>GCF<\/strong>: The GCF is the product of the lowest powers of common prime factors.<br>GCF = 3\u00b2 = 9.<\/p>\n\n\n\n<p><strong>LCM<\/strong>: The LCM is the product of the highest powers of all prime factors.<br>LCM = 2\u00b3 \u00d7 3\u00b2 = 72.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">5. GCF and LCM of 66, 142, 168<\/h3>\n\n\n\n<p><strong>Step 1: Prime Factorization<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>66 = 2 \u00d7 3 \u00d7 11<\/li>\n\n\n\n<li>142 = 2 \u00d7 71<\/li>\n\n\n\n<li>168 = 2\u00b3 \u00d7 3 \u00d7 7<\/li>\n<\/ul>\n\n\n\n<p><strong>GCF<\/strong>: The GCF is the product of the lowest powers of common prime factors.<br>GCF = 2.<\/p>\n\n\n\n<p><strong>LCM<\/strong>: The LCM is the product of the highest powers of all prime factors.<br>LCM = 2\u00b3 \u00d7 3 \u00d7 7 \u00d7 11 \u00d7 71 = 1,1292.<\/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-banner6-1347.jpeg\" alt=\"\" class=\"wp-image-263911\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the Greatest Common Factors and Least Common Multiple of the following numbers: 1. 12, 24, 36 2.. 10, 25, 50 3. 38, 86, 120 4. 9, 36, 72 5. 66, 142, 168 The Correct Answer and Explanation is: To find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of the given numbers, [&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 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