{"id":2027,"date":"2012-06-19T18:20:52","date_gmt":"2012-06-19T18:20:52","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=2027"},"modified":"2014-12-02T08:33:43","modified_gmt":"2014-12-02T08:33:43","slug":"factoring-least-common-multiple","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/06\/19\/factoring-least-common-multiple\/","title":{"rendered":"Factoring: Least Common Multiple"},"content":{"rendered":"<p>The LCM of two numbers x and y is the least number among all the common multiples of x and y.<\/p>\n<p><strong>Example:<\/strong><\/p>\n<p>Find the LCM of 6 and 9.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Multiples of 6 are 6,12,18,24,30,36,\u2026<\/p>\n<p>Multiples of 9 are 9,18,27,36,\u2026<\/p>\n<p>So the common multiples are 18, 36, \u2026<\/p>\n<p>&nbsp;<\/p>\n<p>So, LCM of 6 and 9 is 18.<\/p>\n<p>&nbsp;<\/p>\n<p>Since this is difficult always to write all the multiples especially in case of large numbers, there is a procedure to find LCM.<\/p>\n<p>&nbsp;<\/p>\n<p><strong><span style=\"text-decoration: underline\">Finding LCM:<\/span><\/strong><\/p>\n<p>There are two methods to find LCM.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>a)\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>Division method:<\/strong><\/p>\n<p>The process of finding LCM using common division method is shown through the following example.<\/p>\n<p><strong>Example: <\/strong>Find the LCM of 12 and 45.<\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>LCM = 3 x 4 x 15 = 180.<\/p>\n<p><strong>b)\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><strong>Factorization method:<\/strong><\/p>\n<p>The process of finding LCM using common division method is shown through the following example.<\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p><strong>Example: <\/strong>Find the LCM of 12 and 45.<\/p>\n<p><strong>\u00a0<\/strong><\/p>\n<p>Step-1: Find the prime factorization of the given numbers.<\/p>\n<p>12 =2<sup>2<\/sup> x 3<\/p>\n<p>45 = 3<sup>2<\/sup> x 5<\/p>\n<p>&nbsp;<\/p>\n<p>Step-2: Take the product of highest powers of all the prime numbers involved in the factorizations (from the step 1).<\/p>\n<p>The prime numbers involved in these factorizations are 2,3 and 5 and their highest powers are 2<sup>2<\/sup>, 3<sup>2<\/sup> and 5.<\/p>\n<p>So, LCM of 12 and 45 = 2<sup>2<\/sup> x 3<sup>2<\/sup> x 5 = <strong>180.<\/strong><br \/>\nSchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Yorba Linda visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-yorba-linda-california\/\">Tutoring in Yorba Linda.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The LCM of two numbers x and y is the least number among all the common multiples of x and y. Example: Find the LCM of 6 and 9. &nbsp; Solution: Multiples of 6 are 6,12,18,24,30,36,\u2026 Multiples of 9 are 9,18,27,36,\u2026 So the common multiples are 18, 36, \u2026 &nbsp; So, LCM of 6 and [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,4,13,14],"tags":[320,645,648,1015,1016,1021,1022,1067,1068,1157,1158,1684,1685],"class_list":["post-2027","post","type-post","status-publish","format-standard","hentry","category-algebra","category-calculus","category-pre-algebra","category-pre-calculus","tag-common-multiple","tag-factoring","tag-factorization","tag-lcd","tag-lcm","tag-least-common","tag-least-common-multiple","tag-lowest","tag-lowest-common","tag-multiples","tag-multiples-in-factoring","tag-solve","tag-solve-for"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2027","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=2027"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/2027\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=2027"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=2027"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=2027"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}