{"id":233231,"date":"2025-06-12T20:41:02","date_gmt":"2025-06-12T20:41:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233231"},"modified":"2025-06-12T20:41:04","modified_gmt":"2025-06-12T20:41:04","slug":"find-the-hcf-and-lcm-of-36-54-and-90-using-prime-factorisation-method","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/find-the-hcf-and-lcm-of-36-54-and-90-using-prime-factorisation-method\/","title":{"rendered":"find the HCF and LCM of 36 , 54 and 90 using prime factorisation method"},"content":{"rendered":"\n<p>find the HCF and LCM of 36 , 54 and 90 using prime factorisation method<\/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>HCF (Highest Common Factor)<\/strong> and <strong>LCM (Least Common Multiple)<\/strong> of 36, 54, and 90 using the <strong>prime factorisation method<\/strong>, 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\"><strong>Step 1: Prime factorisation<\/strong><\/h3>\n\n\n\n<p><strong>36<\/strong><br>= 2 \u00d7 2 \u00d7 3 \u00d7 3<br>= 2\u00b2 \u00d7 3\u00b2<\/p>\n\n\n\n<p><strong>54<\/strong><br>= 2 \u00d7 3 \u00d7 3 \u00d7 3<br>= 2 \u00d7 3\u00b3<\/p>\n\n\n\n<p><strong>90<\/strong><br>= 2 \u00d7 3 \u00d7 3 \u00d7 5<br>= 2 \u00d7 3\u00b2 \u00d7 5<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: HCF (Highest Common Factor)<\/strong><\/h3>\n\n\n\n<p>To find the HCF, take the <strong>lowest power of each common prime factor<\/strong>.<\/p>\n\n\n\n<p>Common prime factors: 2 and 3<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 appears as: 2\u00b2 (in 36), 2\u00b9 (in 54), 2\u00b9 (in 90) \u2192 take <strong>2\u00b9<\/strong><\/li>\n\n\n\n<li>3 appears as: 3\u00b2 (in 36), 3\u00b3 (in 54), 3\u00b2 (in 90) \u2192 take <strong>3\u00b2<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So,<br><strong>HCF = 2\u00b9 \u00d7 3\u00b2 = 2 \u00d7 9 = 18<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: LCM (Least Common Multiple)<\/strong><\/h3>\n\n\n\n<p>To find the LCM, take the <strong>highest power of each prime factor<\/strong> that appears in any number.<\/p>\n\n\n\n<p>Prime factors: 2, 3, and 5<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 \u2192 highest power is <strong>2\u00b2<\/strong> (from 36)<\/li>\n\n\n\n<li>3 \u2192 highest power is <strong>3\u00b3<\/strong> (from 54)<\/li>\n\n\n\n<li>5 \u2192 appears only in 90 as <strong>5\u00b9<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So,<br><strong>LCM = 2\u00b2 \u00d7 3\u00b3 \u00d7 5 = 4 \u00d7 27 \u00d7 5 = 540<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Final Answers:<\/strong><\/h3>\n\n\n\n<p><strong>HCF = 18<\/strong><br><strong>LCM = 540<\/strong><\/p>\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>The prime factorisation method is a systematic way to find both the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of a set of numbers. This method involves expressing each number as a product of its prime factors.<\/p>\n\n\n\n<p>First, perform the prime factorisation of each number. For 36, the prime factors are 2\u00b2 \u00d7 3\u00b2. For 54, they are 2 \u00d7 3\u00b3. For 90, the prime factorisation is 2 \u00d7 3\u00b2 \u00d7 5. Once all numbers are expressed in terms of their prime factors, we can proceed to find the HCF and LCM.<\/p>\n\n\n\n<p>To find the HCF, we look for <strong>common prime factors<\/strong> in all three numbers and take the <strong>lowest exponent<\/strong> of each. In this case, the common prime factors are 2 and 3. The lowest power of 2 across all numbers is 1, and for 3, it is 2. Multiplying these gives the HCF as 18.<\/p>\n\n\n\n<p>For the LCM, we consider <strong>all prime factors<\/strong> present in any of the numbers and take the <strong>highest power<\/strong> of each. Here, the highest power of 2 is 2, for 3 it is 3, and 5 appears only once in 90. Thus, multiplying 2\u00b2 \u00d7 3\u00b3 \u00d7 5 gives us 540 as the LCM.<\/p>\n\n\n\n<p>Using this method ensures accuracy because it is based on the fundamental principle that any composite number can be uniquely expressed as a product of primes. It is particularly useful for larger numbers, where listing out factors or multiples is not practical.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-426.jpeg\" alt=\"\" class=\"wp-image-233232\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>find the HCF and LCM of 36 , 54 and 90 using prime factorisation method The Correct Answer and Explanation is: To find the HCF (Highest Common Factor) and LCM (Least Common Multiple) of 36, 54, and 90 using the prime factorisation method, follow these steps: Step 1: Prime factorisation 36= 2 \u00d7 2 \u00d7 [&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-233231","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233231","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=233231"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233231\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233231"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233231"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233231"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}