{"id":223564,"date":"2025-06-02T05:28:05","date_gmt":"2025-06-02T05:28:05","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223564"},"modified":"2025-06-02T05:28:07","modified_gmt":"2025-06-02T05:28:07","slug":"what-number-should-be-subtracted-from-65-to-make-it-divisible-by-6-12-and-15","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/what-number-should-be-subtracted-from-65-to-make-it-divisible-by-6-12-and-15\/","title":{"rendered":"What number should be subtracted from 65 to make it divisible by 6, 12, and 15"},"content":{"rendered":"\n<p>What number should be subtracted from 65 to make it divisible by 6, 12, and 15<\/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 number that should be subtracted from <strong>65<\/strong> to make it divisible by <strong>6<\/strong>, <strong>12<\/strong>, and <strong>15<\/strong>, we follow a systematic approach.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Correct Answer: 5<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 <strong>Step-by-Step Explanation<\/strong><\/h3>\n\n\n\n<p>To solve the problem, we need to <strong>subtract a number from 65<\/strong> so that the result is divisible by <strong>6, 12, and 15<\/strong>. This means the resulting number must be a <strong>common multiple<\/strong> of 6, 12, and 15.<\/p>\n\n\n\n<p>The first step is to <strong>find the Least Common Multiple (LCM)<\/strong> of the three numbers:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\ud83d\udd39 Prime Factorizations:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>6 = 2 \u00d7 3<\/li>\n\n\n\n<li>12 = 2\u00b2 \u00d7 3<\/li>\n\n\n\n<li>15 = 3 \u00d7 5<\/li>\n<\/ul>\n\n\n\n<p>To find the LCM, we take the <strong>highest powers<\/strong> of all prime numbers involved:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2\u00b2 (from 12)<\/li>\n\n\n\n<li>3 (common in all)<\/li>\n\n\n\n<li>5 (from 15)<\/li>\n<\/ul>\n\n\n\n<p><strong>LCM = 2\u00b2 \u00d7 3 \u00d7 5 = 4 \u00d7 3 \u00d7 5 = 60<\/strong><\/p>\n\n\n\n<p>So, the smallest number that is divisible by <strong>6, 12, and 15<\/strong> is <strong>60<\/strong>.<\/p>\n\n\n\n<p>Now, we ask:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>What number should be subtracted from <strong>65<\/strong> to get <strong>60<\/strong>?<\/p>\n<\/blockquote>\n\n\n\n<p>That\u2019s simply:<\/p>\n\n\n\n<p><strong>65 &#8211; 60 = 5<\/strong><\/p>\n\n\n\n<p>So, <strong>5 should be subtracted<\/strong> from 65.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Verification<\/strong><\/h3>\n\n\n\n<p>Let\u2019s check that <strong>60<\/strong> is divisible by 6, 12, and 15:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>60 \u00f7 6 = 10<\/li>\n\n\n\n<li>60 \u00f7 12 = 5<\/li>\n\n\n\n<li>60 \u00f7 15 = 4<\/li>\n<\/ul>\n\n\n\n<p>All results are whole numbers, confirming 60 is divisible by all three.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udde0 Final Thought<\/h3>\n\n\n\n<p>This type of problem tests your understanding of the <strong>Least Common Multiple<\/strong> and <strong>basic arithmetic reasoning<\/strong>. Instead of checking all numbers below 65, using the LCM method saves time and ensures accuracy. This approach is especially useful when dealing with multiple divisibility conditions.<\/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-banner6-10.jpeg\" alt=\"\" class=\"wp-image-223565\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What number should be subtracted from 65 to make it divisible by 6, 12, and 15 The Correct Answer and Explanation is: To find the number that should be subtracted from 65 to make it divisible by 6, 12, and 15, we follow a systematic approach. \u2705 Correct Answer: 5 \ud83d\udcd8 Step-by-Step Explanation To solve [&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-223564","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223564","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=223564"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223564\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223564"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223564"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223564"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}