{"id":245560,"date":"2025-07-06T08:59:41","date_gmt":"2025-07-06T08:59:41","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245560"},"modified":"2025-07-06T08:59:44","modified_gmt":"2025-07-06T08:59:44","slug":"find-the-greatest-common-divisor-of-35-60-and-75-by-the-list-method-factor-tree-division-and-prime-factors-method","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/find-the-greatest-common-divisor-of-35-60-and-75-by-the-list-method-factor-tree-division-and-prime-factors-method\/","title":{"rendered":"Find the Greatest Common Divisor of 35, 60, and 75 by the List Method, Factor Tree Division, and Prime Factors Method"},"content":{"rendered":"\n
6) Find the Greatest Common Divisor of 35, 60, and 75 by the List Method, Factor Tree Division, and Prime Factors Method. 7) Find the Least Common Multiple of 60 and 75 using either the Dividing by Prime Factors Method or the Formula.<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
6) Finding the Greatest Common Divisor (GCD) of 35, 60, and 75<\/strong><\/h3>\n\n\n\n
Method 1: List Method<\/strong> To find the GCD, we first list the factors of each number.<\/p>\n\n\n\n
\n
Factors of 35<\/strong>: 1, 5, 7, 35<\/li>\n\n\n\n
The common prime factor<\/strong> across all three numbers is 5<\/strong>. Therefore, the GCD is 5<\/strong>.<\/p>\n\n\n\n
Method 3: Prime Factors Method<\/strong> From the prime factorization:<\/p>\n\n\n\n
\n
35 = 5 \u00d7 7<\/li>\n\n\n\n
60 = 2\u00b2 \u00d7 3 \u00d7 5<\/li>\n\n\n\n
75 = 3 \u00d7 5\u00b2<\/li>\n<\/ul>\n\n\n\n
The only common prime factor<\/strong> is 5<\/strong>, and the lowest power<\/strong> of 5 is 5\u00b9<\/strong>. Thus, the GCD is 5<\/strong>.<\/p>\n\n\n\n\n\n\n\n
7) Finding the Least Common Multiple (LCM) of 60 and 75<\/strong><\/h3>\n\n\n\n
Method 1: Dividing by Prime Factors Method<\/strong> First, find the prime factorizations of the numbers:<\/p>\n\n\n\n
\n
60 = 2\u00b2 \u00d7 3 \u00d7 5<\/li>\n\n\n\n
75 = 3 \u00d7 5\u00b2<\/li>\n<\/ul>\n\n\n\n
To find the LCM<\/strong>, take the highest powers<\/strong> of all the prime factors:<\/p>\n\n\n\n
So, the LCM of 60 and 75 is 300<\/strong>.<\/p>\n\n\n\n
Method 2: Formula Method<\/strong> The formula for the LCM using the GCD is:LCM(a,b)=\u2223a\u00d7b\u2223GCD(a,b)LCM(a, b) = \\frac{|a \u00d7 b|}{GCD(a, b)}LCM(a,b)=GCD(a,b)\u2223a\u00d7b\u2223\u200b<\/p>\n\n\n\n
Using the previously calculated GCD of 60 and 75<\/strong> (which is 15):LCM(60,75)=\u222360\u00d775\u222315=450015=300LCM(60, 75) = \\frac{|60 \u00d7 75|}{15} = \\frac{4500}{15} = 300LCM(60,75)=15\u222360\u00d775\u2223\u200b=154500\u200b=300<\/p>\n\n\n\n
Thus, the LCM is 300<\/strong>.<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
\n
GCD<\/strong> is the largest number that divides both numbers without leaving a remainder. It shows the greatest shared factor between them.<\/li>\n\n\n\n
LCM<\/strong> is the smallest number that both numbers can divide without leaving a remainder. It’s useful for finding common multiples, especially when working with fractions, ratios, or scheduling problems.<\/li>\n<\/ul>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
6) Find the Greatest Common Divisor of 35, 60, and 75 by the List Method, Factor Tree Division, and Prime Factors Method. 7) Find the Least Common Multiple of 60 and 75 using either the Dividing by Prime Factors Method or the Formula. The Correct Answer and Explanation is: 6) Finding the Greatest Common Divisor […]<\/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-245560","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245560","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=245560"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245560\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245560"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245560"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245560"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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