{"id":230807,"date":"2025-06-10T06:26:36","date_gmt":"2025-06-10T06:26:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230807"},"modified":"2025-06-10T06:26:38","modified_gmt":"2025-06-10T06:26:38","slug":"find-the-lcm-of-45-and-75","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/10\/find-the-lcm-of-45-and-75\/","title":{"rendered":"Find the LCM of 45 and 75."},"content":{"rendered":"\n<p>Find the LCM of 45 and 75. use their LCM to obtain the HCF<\/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><strong>Answer:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>LCM of 45 and 75 = 225<\/strong><\/li>\n\n\n\n<li><strong>HCF of 45 and 75 = 15<\/strong><\/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\">Step-by-Step Solution:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>1. Prime Factorization<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>45 = 3 \u00d7 3 \u00d7 5 = 3\u00b2 \u00d7 5<\/li>\n\n\n\n<li>75 = 3 \u00d7 5 \u00d7 5 = 3 \u00d7 5\u00b2<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>2. Find the LCM (Least Common Multiple)<\/strong><\/h4>\n\n\n\n<p>To find the LCM, take <strong>the highest powers of all prime factors<\/strong> involved.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>LCM = 3\u00b2 \u00d7 5\u00b2 = 9 \u00d7 25 = <strong>225<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>3. Use the relationship between LCM and HCF<\/strong><\/h4>\n\n\n\n<p>There is a key identity that relates LCM and HCF:LCM\u00d7HCF=Product&nbsp;of&nbsp;the&nbsp;two&nbsp;numbers\\text{LCM} \\times \\text{HCF} = \\text{Product of the two numbers}LCM\u00d7HCF=Product&nbsp;of&nbsp;the&nbsp;two&nbsp;numbers<\/p>\n\n\n\n<p>Let\u2019s check:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>45 \u00d7 75 = 3375<\/li>\n\n\n\n<li>LCM = 225 (from step 2)<\/li>\n<\/ul>\n\n\n\n<p>So,HCF=45\u00d775LCM=3375225=15\\text{HCF} = \\frac{45 \\times 75}{\\text{LCM}} = \\frac{3375}{225} = 15HCF=LCM45\u00d775\u200b=2253375\u200b=15<\/p>\n\n\n\n<p>\u2705 Hence, the <strong>HCF of 45 and 75 is 15<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>To find the Least Common Multiple (LCM) of two numbers, you look for the smallest number that both numbers divide into without leaving a remainder. The most efficient way to find the LCM is by using prime factorization. For 45, the prime factors are 3\u00b2 \u00d7 5, and for 75, the prime factors are 3 \u00d7 5\u00b2. To get the LCM, you must take the highest powers of all the prime factors that appear in either number. From both numbers, the highest powers are 3\u00b2 and 5\u00b2. Multiplying these gives the LCM: 3\u00b2 \u00d7 5\u00b2 = 9 \u00d7 25 = 225.<\/p>\n\n\n\n<p>The Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest number that divides both numbers without leaving a remainder. A key mathematical relationship connects the LCM and HCF of any two positive integers:LCM\u00d7HCF=Product&nbsp;of&nbsp;the&nbsp;two&nbsp;numbers\\text{LCM} \\times \\text{HCF} = \\text{Product of the two numbers}LCM\u00d7HCF=Product&nbsp;of&nbsp;the&nbsp;two&nbsp;numbers<\/p>\n\n\n\n<p>Using this relationship, you can derive the HCF from the LCM. Since we already know that the product of 45 and 75 is 3375 and the LCM is 225, dividing the product by the LCM gives the HCF:3375\u00f7225=153375 \\div 225 = 153375\u00f7225=15<\/p>\n\n\n\n<p>This identity is helpful because once you find either the LCM or HCF using one method (such as prime factorization), you can derive the other. This approach is especially useful for large numbers, where direct factoring might be more challenging.<\/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-banner4-793.jpeg\" alt=\"\" class=\"wp-image-230808\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the LCM of 45 and 75. use their LCM to obtain the HCF The Correct Answer and Explanation is: Answer: Step-by-Step Solution: 1. Prime Factorization 2. Find the LCM (Least Common Multiple) To find the LCM, take the highest powers of all prime factors involved. 3. Use the relationship between LCM and HCF There [&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-230807","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230807","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=230807"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230807\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230807"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230807"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230807"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}