{"id":6317,"date":"2022-10-26T10:52:27","date_gmt":"2022-10-26T08:52:27","guid":{"rendered":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/?p=6317"},"modified":"2022-10-26T10:53:07","modified_gmt":"2022-10-26T08:53:07","slug":"lenigma-del-calcul-del-maxim-comu-divisor-i-el-minim-comu-multiple","status":"publish","type":"post","link":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/portada\/lenigma-del-calcul-del-maxim-comu-divisor-i-el-minim-comu-multiple\/","title":{"rendered":"L&#8217;enigma del c\u00e0lcul del M\u00e0xim Com\u00fa Divisor i el M\u00ednim Com\u00fa M\u00faltiple"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">El M\u00e0xim Com\u00fa Divisor i el M\u00ednim Com\u00fa M\u00faltiple s\u00f3n dues eines indispensables per a poder operar i sintetitzar nombres racionals, \u00e9s a dir, per a poder treballar amb fraccions.\u00a0Per aix\u00f2, a 2n d&#8217;ESO, les hem repassat i treballat a fons. Us agradaria saber qu\u00e8 hem descobert?<\/span><\/p>\n<p><b>El M\u00e0xim Com\u00fa Divisor: <\/b><span style=\"font-weight: 400;\">si observem dos nombres naturals donats, sabem que el seu M\u00e0xim Com\u00fa Divisor \u00e9s el nombre m\u00e9s gran capa\u00e7 de dividir un nombre i altre de manera exacta, \u00e9s a dir, sense que, en cap dels dos casos, la seva divisi\u00f3 deixi residu.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Els llibres de text ens diuen que podem calcular el MCD de dos nombres donats com el producte dels seus factors primers comuns elevats al seu menor exponent. Ara b\u00e9: qu\u00e8 representa aquest producte de factors? Per qu\u00e8 justament hem de prendre els exponents m\u00e9s petits dels factors comuns? Sembla un enigma, oi?<\/span><\/p>\n<p><b>El M\u00ednim Com\u00fa M\u00faltiple<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Si observem dos nombres naturals donats, sabem que el seu M\u00ednim Com\u00fa M\u00faltiple \u00e9s el nombre m\u00e9s petit que podem trobar tant en la taula de multiplicar de l\u2019un com en la taula de multiplicar de l\u2019altre.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Els llibres de text ens diuen que podem calcular el MCM de dos nombres donats com el producte dels seus factors primers comuns i no comuns elevats al seu major exponent. Ara b\u00e9: qu\u00e8 representa aquest producte de factors? Per qu\u00e8 justament hem de prendre els exponents m\u00e9s grans dels factors comuns? Per qu\u00e8 hem d\u2019incloure els factors no comuns? <\/span><\/p>\n<p><em>Doncs aix\u00f2 hem fet a classe, per despertar la passi\u00f3 per les matem\u00e0tiques a partir d&#8217;aquests enigmes.<\/em><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-6319\" src=\"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_1.jpeg\" alt=\"\" width=\"1672\" height=\"1254\" srcset=\"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_1.jpeg 1672w, https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_1-300x225.jpeg 300w, https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_1-1024x768.jpeg 1024w, https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_1-768x576.jpeg 768w, https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_1-1536x1152.jpeg 1536w, https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_1-200x150.jpeg 200w\" sizes=\"auto, (max-width: 1672px) 100vw, 1672px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-6318\" src=\"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_2.jpeg\" alt=\"\" width=\"1672\" height=\"1254\" srcset=\"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_2.jpeg 1672w, https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_2-300x225.jpeg 300w, https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_2-1024x768.jpeg 1024w, https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_2-768x576.jpeg 768w, https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_2-1536x1152.jpeg 1536w, https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-content\/uploads\/usu44\/2022\/10\/MCD_2-200x150.jpeg 200w\" sizes=\"auto, (max-width: 1672px) 100vw, 1672px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>El M\u00e0xim Com\u00fa Divisor i el M\u00ednim Com\u00fa M\u00faltiple s\u00f3n dues eines indispensables per a poder operar i sintetitzar nombres racionals, \u00e9s a dir, per a poder treballar amb fraccions.\u00a0Per aix\u00f2, a 2n d&#8217;ESO, les hem repassat i treballat a fons. Us agradaria saber qu\u00e8 hem descobert? El M\u00e0xim Com\u00fa Divisor: si observem dos nombres [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":6319,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[99,29],"tags":[41],"class_list":["post-6317","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-activitats","category-portada","tag-matematiques"],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/posts\/6317","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/comments?post=6317"}],"version-history":[{"count":1,"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/posts\/6317\/revisions"}],"predecessor-version":[{"id":6320,"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/posts\/6317\/revisions\/6320"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/media\/6319"}],"wp:attachment":[{"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/media?parent=6317"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/categories?post=6317"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/agora.xtec.cat\/ies-santaeulalia\/wp-json\/wp\/v2\/tags?post=6317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}