{"id":40606,"date":"2025-06-27T18:47:50","date_gmt":"2025-06-27T18:47:50","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=40606"},"modified":"2025-06-27T18:47:55","modified_gmt":"2025-06-27T18:47:55","slug":"find-the-lcm-and-hcf-of-72-80-and-120-by-applying-prime-factorization","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-lcm-and-hcf-of-72-80-and-120-by-applying-prime-factorization\/","title":{"rendered":"Find the LCM and HCF of 72, 80, and 120 by applying prime factorization"},"content":{"rendered":"\n<p>Find the LCM and HCF of 72, 80, and 120 by applying prime factorization.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>HCF (Highest Common Factor)<\/strong> = 8<\/li>\n\n\n\n<li><strong>LCM (Lowest Common Multiple)<\/strong> = 720<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation:<\/strong><\/h3>\n\n\n\n<p>To find the <strong>HCF<\/strong> and <strong>LCM<\/strong> of 72, 80, and 120 using <strong>prime factorization<\/strong>, start by breaking each number into its prime factors:<\/p>\n\n\n\n<p><strong>1. Prime Factorization:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>72<\/strong> = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 = 2\u00b3 \u00d7 3\u00b2<\/li>\n\n\n\n<li><strong>80<\/strong> = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 5 = 2\u2074 \u00d7 5<\/li>\n\n\n\n<li><strong>120<\/strong> = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 5 = 2\u00b3 \u00d7 3 \u00d7 5<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>2. HCF (Greatest Common Factor):<\/strong><\/p>\n\n\n\n<p>To find the HCF, take the <strong>lowest powers<\/strong> of all <strong>common prime factors<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The common prime factor among all three numbers is 2.<\/li>\n\n\n\n<li>The lowest power of 2 that appears in all is 2\u00b3.<\/li>\n<\/ul>\n\n\n\n<p>There are no other common prime factors among all three numbers.<\/p>\n\n\n\n<p><strong>Therefore, HCF = 2\u00b3 = 8<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>3. LCM (Lowest Common Multiple):<\/strong><\/p>\n\n\n\n<p>To find the LCM, take the <strong>highest powers<\/strong> of <strong>all prime factors<\/strong> that appear in any of the numbers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Prime factor 2: highest power is 2\u2074 (from 80)<\/li>\n\n\n\n<li>Prime factor 3: highest power is 3\u00b2 (from 72)<\/li>\n\n\n\n<li>Prime factor 5: highest power is 5 (from 80 and 120)<\/li>\n<\/ul>\n\n\n\n<p>Now multiply these together:<\/p>\n\n\n\n<p><strong>LCM = 2\u2074 \u00d7 3\u00b2 \u00d7 5 = 16 \u00d7 9 \u00d7 5 = 720<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Conclusion:<\/strong><\/p>\n\n\n\n<p>Using prime factorization, the HCF of 72, 80, and 120 is <strong>8<\/strong>, and the LCM is <strong>720<\/strong>. Prime factorization makes it easier to see the structure of each number and determine both the highest common factor and the least common multiple by comparing prime powers.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the LCM and HCF of 72, 80, and 120 by applying prime factorization. The correct answer and explanation is: Correct Answer: Explanation: To find the HCF and LCM of 72, 80, and 120 using prime factorization, start by breaking each number into its prime factors: 1. Prime Factorization: 2. HCF (Greatest Common Factor): To [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-40606","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40606","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=40606"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40606\/revisions"}],"predecessor-version":[{"id":40607,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/40606\/revisions\/40607"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=40606"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=40606"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=40606"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}