{"id":9446,"date":"2017-05-02T22:33:53","date_gmt":"2017-05-02T22:33:53","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9446"},"modified":"2020-01-09T01:35:44","modified_gmt":"2020-01-09T01:35:44","slug":"summary-prime-factorization-and-the-least-common-multiple","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/chapter\/summary-prime-factorization-and-the-least-common-multiple\/","title":{"raw":"Summary: Prime Factorization and the Least Common Multiple","rendered":"Summary: Prime Factorization and the Least Common Multiple"},"content":{"raw":"<h1 style=\"text-align: center;\"><span style=\"color: #ff0000; background-color: #999999;\">End of textbook section. After reviewing the content below,\r\nClose this tab and proceed to the assignment\u00a0<\/span><\/h1>\r\n<h2>Key Concepts<\/h2>\r\n<ul id=\"fs-id2657539\">\r\n \t<li><strong>Find the prime factorization of a composite number using the tree method.<\/strong>\r\n<ol id=\"eip-id1170195278180\" class=\"stepwise\">\r\n \t<li>Find any factor pair of the given number, and use these numbers to create two branches.<\/li>\r\n \t<li>If a factor is prime, that branch is complete. Circle the prime.<\/li>\r\n \t<li>If a factor is not prime, write it as the product of a factor pair and continue the process.<\/li>\r\n \t<li>Write the composite number as the product of all the circled primes.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Find the prime factorization of a composite number using the ladder method.<\/strong>\r\n<ol id=\"eip-id1170195278197\" class=\"stepwise\">\r\n \t<li>Divide the number by the smallest prime.<\/li>\r\n \t<li>Continue dividing by that prime until it no longer divides evenly.<\/li>\r\n \t<li>Divide by the next prime until it no longer divides evenly.<\/li>\r\n \t<li>Continue until the quotient is a prime.<\/li>\r\n \t<li>Write the composite number as the product of all the primes on the sides and top of the ladder.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Find the LCM using the prime factors method.<\/strong>\r\n<ol id=\"eip-id1170195278218\" class=\"stepwise\">\r\n \t<li>Find the prime factorization of each number.<\/li>\r\n \t<li>Write each number as a product of primes, matching primes vertically when possible.<\/li>\r\n \t<li>Bring down the primes in each column.<\/li>\r\n \t<li>Multiply the factors to get the LCM.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Find the LCM using the prime factors method.<\/strong>\r\n<ol id=\"eip-id1170195278236\" class=\"stepwise\">\r\n \t<li>Find the prime factorization of each number.<\/li>\r\n \t<li>Write each number as a product of primes, matching primes vertically when possible.<\/li>\r\n \t<li>Bring down the primes in each column.<\/li>\r\n \t<li>Multiply the factors to get the LCM.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\r\n<dl id=\"fs-id1596534\" class=\"definition\">\r\n \t<dt><strong>multiple of a number<\/strong><\/dt>\r\n \t<dd id=\"fs-id1596539\">A number is a multiple of [latex]n[\/latex] if it is the product of a counting number and [latex]n[\/latex] .<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1596543\" class=\"definition\">\r\n \t<dt><strong>divisibility<\/strong><\/dt>\r\n \t<dd id=\"fs-id2860656\">If a number [latex]m[\/latex] is a multiple of [latex]n[\/latex] , then we say that [latex]m[\/latex] is divisible by [latex]n[\/latex] .<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id2860661\" class=\"definition\">\r\n \t<dt><strong>prime number<\/strong><\/dt>\r\n \t<dd id=\"fs-id2860666\">A prime number is a counting number greater than 1 whose only factors are 1 and itself.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1227087\" class=\"definition\">\r\n \t<dt><strong>composite number<\/strong><\/dt>\r\n \t<dd id=\"fs-id1227093\">A composite number is a counting number that is not prime.<\/dd>\r\n<\/dl>","rendered":"<h1 style=\"text-align: center;\"><span style=\"color: #ff0000; background-color: #999999;\">End of textbook section. After reviewing the content below,<br \/>\nClose this tab and proceed to the assignment\u00a0<\/span><\/h1>\n<h2>Key Concepts<\/h2>\n<ul id=\"fs-id2657539\">\n<li><strong>Find the prime factorization of a composite number using the tree method.<\/strong>\n<ol id=\"eip-id1170195278180\" class=\"stepwise\">\n<li>Find any factor pair of the given number, and use these numbers to create two branches.<\/li>\n<li>If a factor is prime, that branch is complete. Circle the prime.<\/li>\n<li>If a factor is not prime, write it as the product of a factor pair and continue the process.<\/li>\n<li>Write the composite number as the product of all the circled primes.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Find the prime factorization of a composite number using the ladder method.<\/strong>\n<ol id=\"eip-id1170195278197\" class=\"stepwise\">\n<li>Divide the number by the smallest prime.<\/li>\n<li>Continue dividing by that prime until it no longer divides evenly.<\/li>\n<li>Divide by the next prime until it no longer divides evenly.<\/li>\n<li>Continue until the quotient is a prime.<\/li>\n<li>Write the composite number as the product of all the primes on the sides and top of the ladder.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Find the LCM using the prime factors method.<\/strong>\n<ol id=\"eip-id1170195278218\" class=\"stepwise\">\n<li>Find the prime factorization of each number.<\/li>\n<li>Write each number as a product of primes, matching primes vertically when possible.<\/li>\n<li>Bring down the primes in each column.<\/li>\n<li>Multiply the factors to get the LCM.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Find the LCM using the prime factors method.<\/strong>\n<ol id=\"eip-id1170195278236\" class=\"stepwise\">\n<li>Find the prime factorization of each number.<\/li>\n<li>Write each number as a product of primes, matching primes vertically when possible.<\/li>\n<li>Bring down the primes in each column.<\/li>\n<li>Multiply the factors to get the LCM.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl id=\"fs-id1596534\" class=\"definition\">\n<dt><strong>multiple of a number<\/strong><\/dt>\n<dd id=\"fs-id1596539\">A number is a multiple of [latex]n[\/latex] if it is the product of a counting number and [latex]n[\/latex] .<\/dd>\n<\/dl>\n<dl id=\"fs-id1596543\" class=\"definition\">\n<dt><strong>divisibility<\/strong><\/dt>\n<dd id=\"fs-id2860656\">If a number [latex]m[\/latex] is a multiple of [latex]n[\/latex] , then we say that [latex]m[\/latex] is divisible by [latex]n[\/latex] .<\/dd>\n<\/dl>\n<dl id=\"fs-id2860661\" class=\"definition\">\n<dt><strong>prime number<\/strong><\/dt>\n<dd id=\"fs-id2860666\">A prime number is a counting number greater than 1 whose only factors are 1 and itself.<\/dd>\n<\/dl>\n<dl id=\"fs-id1227087\" class=\"definition\">\n<dt><strong>composite number<\/strong><\/dt>\n<dd id=\"fs-id1227093\">A composite number is a counting number that is not prime.<\/dd>\n<\/dl>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-9446\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17535,"menu_order":13,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","CANDELA_OUTCOMES_GUID":"710ef196-5762-4acd-9a7e-091abb61ba29","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9446","chapter","type-chapter","status-publish","hentry"],"part":16105,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9446","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/users\/17535"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9446\/revisions"}],"predecessor-version":[{"id":16123,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9446\/revisions\/16123"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/parts\/16105"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9446\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/media?parent=9446"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9446"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/contributor?post=9446"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/csn-prealgebra\/wp-json\/wp\/v2\/license?post=9446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}