{"id":104,"date":"2005-12-10T20:32:52","date_gmt":"2005-12-10T20:32:52","guid":{"rendered":"http:\/\/www.sixthform.info\/maths\/?p=104"},"modified":"2005-12-10T20:32:52","modified_gmt":"2005-12-10T20:32:52","slug":"problem","status":"publish","type":"post","link":"https:\/\/www.sixthform.info\/maths\/?p=104","title":{"rendered":"Problem"},"content":{"rendered":"<p>There was a nice little problem posted on <a href=\"http:\/\/www.sosmath.com\/CBB\/\" target=\"_blank\">S.O.S. Mathematics CyberBoard<\/a> which comes from an <a href=\"http:\/\/www.amt.canberra.edu.au\/imtot.html\" target=\"_blank\">International Mathematics Tournament of Towns<\/a> question:<\/p>\n<ul><i>The least common multiple of positive integers <img src='\/maths\/latexrender\/pictures\/a44c56c8177e32d3613988f4dba7962e.gif' title='a,b,c' alt='a,b,c' align=absmiddle> and <img src='\/maths\/latexrender\/pictures\/8277e0910d750195b448797616e091ad.gif' title='d' alt='d' align=absmiddle> is equal to <img src='\/maths\/latexrender\/pictures\/0c0ed323f7f1a337421b485b1a0c4bea.gif' title='a+b+c+d' alt='a+b+c+d' align=absmiddle>. Prove that the product <img src='\/maths\/latexrender\/pictures\/e2fc714c4727ee9395f324cd2e7f331f.gif' title='abcd' alt='abcd' align=absmiddle> is divisible by at least one of <img src='\/maths\/latexrender\/pictures\/eccbc87e4b5ce2fe28308fd9f2a7baf3.gif' title='3' alt='3' align=absmiddle> and <img src='\/maths\/latexrender\/pictures\/e4da3b7fbbce2345d7772b0674a318d5.gif' title='5' alt='5' align=absmiddle>.<\/i><\/ul>\n<p>If you need a hint you&#8217;ll find one on the <a href=\"http:\/\/www.artofproblemsolving.com\/Forum\/post-317673.html&#038;highlight=lcm#317673\" target=\"_blank\">AoPS Math Forum<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>There was a nice little problem posted on S.O.S. Mathematics CyberBoard which comes from an International Mathematics Tournament of Towns question: The least common multiple of positive integers and is equal to . Prove that the product is divisible by at least one of and . If you need a hint you&#8217;ll find one on [&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-104","post","type-post","status-publish","format-standard","hentry","category-articles"],"_links":{"self":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=104"}],"version-history":[{"count":0,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=\/wp\/v2\/posts\/104\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=104"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=104"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sixthform.info\/maths\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}