{"id":244,"date":"2024-10-18T21:15:17","date_gmt":"2024-10-18T21:15:17","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/chapter\/probability-background-youll-need-2\/"},"modified":"2024-10-18T21:15:17","modified_gmt":"2024-10-18T21:15:17","slug":"probability-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/chapter\/probability-background-youll-need-2\/","title":{"raw":"Probability: Background You'll Need 2","rendered":"Probability: Background You&#8217;ll Need 2"},"content":{"raw":"\n<section class=\"textbox learningGoals\">\n<ul>\n\t<li>Find the smallest number that goes into two numbers<\/li>\n<\/ul>\n<\/section>\n<h2>Find the Least Common Multiple (LCM) of Two Numbers<\/h2>\n<p>The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the numbers in question. It's an important concept that's particularly useful when solving problems involving fractions, ratios, or when finding equivalent fractions.<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How To: Find the Least Common Multiple (LCM)<\/strong><\/p>\n<ol>\n\t<li><strong>List the Multiples<\/strong>: Start by listing a set of multiples for each number. Remember, multiples are what you get when you multiply the number by [latex]1, 2, 3,[\/latex] and so on.<\/li>\n\t<li><strong>Scan for Common Ground<\/strong>: Look for multiples that appear in both lists. These are the common multiples. If you don't find any, continue listing more multiples for each number until you do.<\/li>\n\t<li><strong>Identify the Least<\/strong>: Among the common multiples, pinpoint the smallest one. This is the LCM. It's the \"least common\" because it's the smallest number that all the original numbers can divide into without leaving a remainder.<\/li>\n\t<li><strong>Confirmation<\/strong>: Ensure the number you've identified as the LCM is the smallest common multiple. There can be larger common multiples, but the LCM is always the smallest of these<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\">\n<p>List the first several multiples of [latex]15[\/latex] and of [latex]20[\/latex]. Identify the first common multiple.<\/p>\n<p>[reveal-answer q=\"337383\"]Show Answer[\/reveal-answer]<br>\n[hidden-answer a=\"337383\"]<\/p>\n<p>[latex]\\begin{array}{l}\\text{15: }15,30,45,60,75,90,105,120\\hfill \\\\ \\text{20: }20,40,60,80,100,120,140,160\\hfill \\end{array}[\/latex]<\/p>\n<p>The smallest number to appear on both lists is [latex]60[\/latex], so [latex]60[\/latex] is the least common multiple of [latex]15[\/latex] and [latex]20[\/latex].<\/p>\n<p>Notice that [latex]120[\/latex] is on both lists, too. It is a common multiple, but it is not the least common multiple.<\/p>\n<p>[\/hidden-answer]<\/p>\n<\/section>\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2789[\/ohm2_question]<\/section>\n","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Find the smallest number that goes into two numbers<\/li>\n<\/ul>\n<\/section>\n<h2>Find the Least Common Multiple (LCM) of Two Numbers<\/h2>\n<p>The Least Common Multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the numbers in question. It&#8217;s an important concept that&#8217;s particularly useful when solving problems involving fractions, ratios, or when finding equivalent fractions.<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How To: Find the Least Common Multiple (LCM)<\/strong><\/p>\n<ol>\n<li><strong>List the Multiples<\/strong>: Start by listing a set of multiples for each number. Remember, multiples are what you get when you multiply the number by [latex]1, 2, 3,[\/latex] and so on.<\/li>\n<li><strong>Scan for Common Ground<\/strong>: Look for multiples that appear in both lists. These are the common multiples. If you don&#8217;t find any, continue listing more multiples for each number until you do.<\/li>\n<li><strong>Identify the Least<\/strong>: Among the common multiples, pinpoint the smallest one. This is the LCM. It&#8217;s the &#8220;least common&#8221; because it&#8217;s the smallest number that all the original numbers can divide into without leaving a remainder.<\/li>\n<li><strong>Confirmation<\/strong>: Ensure the number you&#8217;ve identified as the LCM is the smallest common multiple. There can be larger common multiples, but the LCM is always the smallest of these<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\">\n<p>List the first several multiples of [latex]15[\/latex] and of [latex]20[\/latex]. Identify the first common multiple.<\/p>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q337383\">Show Answer<\/button><\/p>\n<div id=\"q337383\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]\\begin{array}{l}\\text{15: }15,30,45,60,75,90,105,120\\hfill \\\\ \\text{20: }20,40,60,80,100,120,140,160\\hfill \\end{array}[\/latex]<\/p>\n<p>The smallest number to appear on both lists is [latex]60[\/latex], so [latex]60[\/latex] is the least common multiple of [latex]15[\/latex] and [latex]20[\/latex].<\/p>\n<p>Notice that [latex]120[\/latex] is on both lists, too. It is a common multiple, but it is not the least common multiple.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2789\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2789&theme=lumen&iframe_resize_id=ohm2789&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":6,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":241,"module-header":"","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/244"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/244\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/parts\/241"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/244\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/media?parent=244"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapter-type?post=244"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/contributor?post=244"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/license?post=244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}