{"id":120730,"date":"2019-03-09T14:52:13","date_gmt":"2019-03-09T17:52:13","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=120730"},"modified":"2023-05-22T06:52:52","modified_gmt":"2023-05-22T09:52:52","slug":"probleminha-menor-multiplo","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/probleminha-menor-multiplo\/","title":{"rendered":".Probleminha:  Menor m\u00faltiplo"},"content":{"rendered":"<p style=\"margin:10px\">\n<div class=\"g1n\" style=\"line-height:27px;\">\n<p class=\"tit\" style=\"line-height:25px;margin:10px\">Problema<br \/>\n<span style=\"font-size:12px;color:#800000\"> (Indicado a partir do 6\u00ba ano do E. F.)<\/span><\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p>Encontre o menor n\u00famero natural n\u00e3o nulo que seja divis\u00edvel por [tex]2, 3, 4, 5, 6[\/tex] e [tex]7[\/tex].<\/p>\n<p style=\"margin:10px\">\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g1n\" style=\"line-height:27px;\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Solu\u00e7\u00e3o 1 <\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p>Note que o n\u00famero [tex]2\\times 3 \\times 4 \\times 5 \\times 6 \\times 7=5040[\/tex] \u00e9 divis\u00edvel por [tex]2, 3, 4, 5, 6[\/tex] e [tex]7[\/tex], mas n\u00e3o \u00e9 o menor natural com esta propriedade: note que repetimos o fator [tex]2[\/tex] ao utilizarmos os n\u00fameros [tex]2, 4[\/tex] e [tex]6[\/tex] e o fator  [tex]3[\/tex] ao utilizarmos os n\u00fameros [tex]3[\/tex]  e [tex]6[\/tex].<br \/>\nAo eliminarmos as repeti\u00e7\u00f5es do  [tex]2[\/tex] e do  [tex]3[\/tex], obtemos o menor n\u00famero com a propriedade requerida: [tex]4\\times 3 \\times 5 \\times 7=\\boxed{420}.[\/tex]<\/p>\n<p style=\"margin:10px; font-size:12px; \">\nRelembrando, o n\u00famero [tex]420[\/tex] \u00e9 o que chamamos na Matem\u00e1tica de o &quot; M\u00ednimo M\u00faltiplo Comum &quot; dos n\u00fameros [tex]2, 3, 4, 5, 6[\/tex] e [tex]7[\/tex]. Denotamos essa propriedade como [tex]420= MMC(2, 3, 4, 5, 6, 7).[\/tex]<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pelos <strong>Moderadores do Blog<\/strong>.<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g1n\" style=\"line-height:27px;\">\n<p class=\"tit\" style=\"line-height:30px;margin:10px\">Solu\u00e7\u00e3o 2 <\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 20px;border: 0 none\"\/>\n<p>Fatorando simultaneamente os algarismos [tex]2,3,4,5,6[\/tex] e [tex]7[\/tex] obtemos o MMC desses n\u00fameros:<\/p>\n<p style=\"margin:10px\">\n[tex]\\qquad \\begin{array}{r r r r  r  r |l}<br \/>\n2 &#038;   3 &#038;  4 &#038;  5 &#038; 6 &#038; 7 &#038;2\\\\<br \/>\n1 &#038; 3 &#038; 2 &#038; 5 &#038; 3 &#038; 7 &#038; 2\\\\<br \/>\n1 &#038; 3 &#038; 1 &#038; 5 &#038; 3 &#038; 7 &#038;3\\\\<br \/>\n1 &#038; 1 &#038; 1 &#038; 5 &#038; 1 &#038; 7 &#038;5\\\\<br \/>\n1 &#038; 1 &#038; 1 &#038; 1 &#038; 1 &#038; 7 &#038;7\\\\<br \/>\n1 &#038; 1 &#038; 1 &#038; 1 &#038; 1&#038; 1\\\\<br \/>\n\\end{array}[\/tex]<\/p>\n<p>Assim,<br \/>\n[tex]\\qquad mmc(2,3,4,5,6,7)=420.[\/tex]<br \/>\nLogo, o menor n\u00famero natural divis\u00edvel por [tex]2,3,4,5,6[\/tex] e [tex]7[\/tex] \u00e9 [tex]420.[\/tex]<\/p>\n<hr style=\"height:1px; width:100%;background-color:#800000; margin-top: 10px; margin-bottom: 15px;border: 0 none\"\/>\n<p class=\"g2\" style=\"line-height:20px;\">Solu\u00e7\u00e3o elaborada pelo <strong>COM OCTETO MATEM\u00c1TICO<\/strong>,  com contribui\u00e7\u00f5es dos Moderadores do Blog.<\/p>\n<\/div>\n<p style=\"margin:30px\">\n<div class=\"g3\">\nParticiparam da discuss\u00e3o os Clubes: <strong>Alfa Club<\/strong> ; <strong>OCTETO MATEM\u00c1TICO<\/strong>.<\/div>\n<p style=\"margin:10px\">\n","protected":false},"excerpt":{"rendered":"<p>Problema (Indicado a partir do 6\u00ba ano do E. F.) Encontre o menor n\u00famero natural n\u00e3o nulo que seja divis\u00edvel por [tex]2, 3, 4, 5, 6[\/tex] e [tex]7[\/tex]. Solu\u00e7\u00e3o 1 Note que o n\u00famero [tex]2\\times 3 \\times 4 \\times 5 \\times 6 \\times 7=5040[\/tex] \u00e9 divis\u00edvel por [tex]2, 3, 4, 5, 6[\/tex] e [tex]7[\/tex], mas &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/probleminha-menor-multiplo\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":667,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-120730","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/120730","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/667"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=120730"}],"version-history":[{"count":25,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/120730\/revisions"}],"predecessor-version":[{"id":124924,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/120730\/revisions\/124924"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=120730"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}