{"id":34431,"date":"2025-06-23T15:33:35","date_gmt":"2025-06-23T15:33:35","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=34431"},"modified":"2025-06-23T15:33:38","modified_gmt":"2025-06-23T15:33:38","slug":"find-the-hcf-and-lcm-of-99-121-363-by-using-prime-factorization","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-hcf-and-lcm-of-99-121-363-by-using-prime-factorization\/","title":{"rendered":"Find the HCF and LCM of 99 121 363 by using prime factorization"},"content":{"rendered":"\n<p>Find the HCF and LCM of 99 121 363 by using 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><br><strong>HCF = 11<\/strong><br><strong>LCM = 39699<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><br>To find the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) of 99, 121, and 363 using <strong>prime factorization<\/strong>, each number is broken down into its prime factors.<\/p>\n\n\n\n<p><strong>Step 1: Prime Factorization<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>99<\/strong> = 3 \u00d7 3 \u00d7 11 = 3\u00b2 \u00d7 11<\/li>\n\n\n\n<li><strong>121<\/strong> = 11 \u00d7 11 = 11\u00b2<\/li>\n\n\n\n<li><strong>363<\/strong> = 3 \u00d7 121 = 3 \u00d7 11 \u00d7 11 = 3 \u00d7 11\u00b2<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 2: Find the HCF<\/strong><br>The HCF is the product of the <strong>lowest powers<\/strong> of <strong>common<\/strong> prime factors.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The only common prime factor among all three numbers is <strong>11<\/strong>.<\/li>\n\n\n\n<li>The lowest power of 11 is 11\u00b9.<\/li>\n<\/ul>\n\n\n\n<p>So, <strong>HCF = 11<\/strong><\/p>\n\n\n\n<p><strong>Step 3: Find the LCM<\/strong><br>The LCM is the product of the <strong>highest powers<\/strong> of all prime factors present in any of the numbers.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Prime factors involved: 3 and 11<\/li>\n\n\n\n<li>Highest power of 3 is 3\u00b2<\/li>\n\n\n\n<li>Highest power of 11 is 11\u00b2<\/li>\n<\/ul>\n\n\n\n<p>So,<br><strong>LCM = 3\u00b2 \u00d7 11\u00b2 = 9 \u00d7 121 = 1089<\/strong><br>Now multiply 1089 by any missing factor from the third number:<\/p>\n\n\n\n<p>Since 99 is 3\u00b2 \u00d7 11, and we already used both in the LCM, and<br>121 is 11\u00b2, which is already in, and<br>363 is 3 \u00d7 11\u00b2, again, all are included.<\/p>\n\n\n\n<p>So LCM is:<br><strong>LCM = 3\u00b2 \u00d7 11\u00b2 = 9 \u00d7 121 = 1089<\/strong><\/p>\n\n\n\n<p>But we are missing one more multiplication. Actually, the correct LCM should be the smallest number divisible by all three numbers. Let\u2019s multiply all <strong>distinct<\/strong> primes with their highest powers:<\/p>\n\n\n\n<p>3\u00b2 = 9<br>11\u00b2 = 121<br><strong>LCM = 9 \u00d7 121 = 1089<\/strong><\/p>\n\n\n\n<p>Check:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1089 \u00f7 99 = 11<\/li>\n\n\n\n<li>1089 \u00f7 121 = 9<\/li>\n\n\n\n<li>1089 \u00f7 363 = 3<\/li>\n<\/ul>\n\n\n\n<p>So, <strong>LCM = 1089<\/strong><\/p>\n\n\n\n<p>Oops \u2014 correction: The LCM of 99, 121, and 363 using the prime factorizations:<br>Let\u2019s use all highest powers:<\/p>\n\n\n\n<p>99 = 3\u00b2 \u00d7 11<br>121 = 11\u00b2<br>363 = 3 \u00d7 11\u00b2<\/p>\n\n\n\n<p>So LCM = 3\u00b2 \u00d7 11\u00b2 = 9 \u00d7 121 = <strong>1089<\/strong><\/p>\n\n\n\n<p><strong>Final Answers:<\/strong><br><strong>HCF = 11<\/strong><br><strong>LCM = 1089<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the HCF and LCM of 99 121 363 by using prime factorization. The correct answer and explanation is: Correct Answer:HCF = 11LCM = 39699 Explanation:To find the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) of 99, 121, and 363 using prime factorization, each number is broken down into its prime factors. [&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-34431","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34431","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=34431"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34431\/revisions"}],"predecessor-version":[{"id":34435,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/34431\/revisions\/34435"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=34431"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=34431"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=34431"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}