{"id":3196,"date":"2020-08-20T15:11:08","date_gmt":"2020-08-20T13:11:08","guid":{"rendered":"https:\/\/www.mathweb.fr\/euclide\/?page_id=3196"},"modified":"2023-04-16T16:18:16","modified_gmt":"2023-04-16T14:18:16","slug":"determiner-le-plus-grand-multiple-dun-nombre-inferieur-a-un-autre-en-python","status":"publish","type":"page","link":"https:\/\/www.mathweb.fr\/euclide\/determiner-le-plus-grand-multiple-dun-nombre-inferieur-a-un-autre-en-python\/","title":{"rendered":"D\u00e9terminer le plus grand multiple d&#8217;un nombre inf\u00e9rieur \u00e0 un autre en Python"},"content":{"rendered":"\n<p>Afin de d\u00e9terminer le plus grand multiple d&#8217;un nombre inf\u00e9rieur \u00e0 un autre en Python, il faut savoir comment v\u00e9rifier si deux nombres sont bel et bien multiples. Il faut aussi avoir une id\u00e9e de la fa\u00e7on dont on peut s&#8217;y prendre du point de vue algorithmique.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"640\" src=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/08\/Python-multiple-inferieur-1024x640.png\" alt=\"plus grand multiple inf\u00e9rieur \u00e0 un autre en Python\" class=\"wp-image-3198\" srcset=\"https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/08\/Python-multiple-inferieur-1024x640.png 1024w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/08\/Python-multiple-inferieur-300x188.png 300w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/08\/Python-multiple-inferieur-600x375.png 600w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/08\/Python-multiple-inferieur-768x480.png 768w, https:\/\/www.mathweb.fr\/euclide\/wp-content\/uploads\/2020\/08\/Python-multiple-inferieur.png 1080w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Approche math\u00e9matique pour d\u00e9terminer le plus grand multiple d&#8217;un nombre inf\u00e9rieur \u00e0 un autre en Python<\/h2>\n\n\n\n<p>Un nombre <em>n<\/em> est multiple d&#8217;un nombre <em>a<\/em> quand le reste de la division de <em>n<\/em> par <em>a<\/em> vaut 0. En Python, cela s&#8217;\u00e9crit :<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"false\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">n % a == 0<\/pre>\n\n\n\n<p>Ainsi, pour d\u00e9terminer le plus grand multiple d&#8217;un nombre <em>a<\/em> inf\u00e9rieur \u00e0 un autre nombre <em>b<\/em>, on peut partir de <em>a<\/em> + 1 et parcourir tous les nombres entiers jusqu&#8217;\u00e0 <em>b<\/em> en testant s&#8217;ils divisent <em>a<\/em>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">D\u00e9terminer le plus grand multiple d&#8217;un nombre inf\u00e9rieur \u00e0 un autre : programmes Python<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Par balayage<\/h3>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">def multiple(a,b):\n    m = 0\n    n = a + 1\n    while n &lt; b:\n        if n % a == 0:\n            m = n\n        n = n + 1\n        \n    return m<\/pre>\n\n\n\n<p>Cette fonction retourne le plus grand multiple du nombre <em>a<\/em> plus petit que <em>b<\/em>. Par exemple,<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">>>> multiple(13,100)\n91<\/pre>\n\n\n\n<p>Cela signifie que le plus grand multiple de 13 inf\u00e9rieur \u00e0 100 est 91.<\/p>\n\n\n\n<p>L&#8217;id\u00e9e ici est donc de balayer tous les nombres entiers \u00e0 partir de <em>a<\/em> + 1 jusqu&#8217;\u00e0 <em>b<\/em>, nombres que l&#8217;on va stocker dans la variable <em>n<\/em>, et pour chacun d&#8217;eux, de tester s&#8217;ils sont multiples de <em>a<\/em> (\u2192 ligne 5). Si tel est le cas, on affecte \u00e0 la variable <em>m<\/em> la valeur du nombre <em>n<\/em> (\u2192 ligne 6).<\/p>\n\n\n\n<p>Cette m\u00e9thode est certes efficace (elle fonctionne quoi !) mais lente car si <em>b<\/em> est extr\u00eamement grand, cela risque de prendre du temps pour y arriver.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Autre m\u00e9thode<\/h3>\n\n\n\n<p>Une autre m\u00e9thode permettant de d\u00e9terminer le plus grand multiple d&#8217;un nombre inf\u00e9rieur \u00e0 un autre en Python consiste \u00e0 simplement multiplier <em>a<\/em> par 2, 3, 4, &#8230; jusqu&#8217;\u00e0 atteindre <em>b<\/em>.<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\" data-enlighter-theme=\"dracula\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">def multiple_bis(a,b):\n    k = 1\n    while a * k &lt; b:\n        k = k + 1\n        \n    return a * (k-1)<\/pre>\n\n\n\n<p>Dans cette derni\u00e8re fonction, <em>k<\/em> joue le r\u00f4le d&#8217;un coefficient multipli\u00e9 \u00e0 <em>a<\/em>. Tant que <em>ka<\/em> &lt; <em>b<\/em>, on ajoute 1 \u00e0 <em>k<\/em>; on sort donc de la boucle <em>while<\/em> quand <em>ka<\/em> \u2265 <em>b<\/em>. <\/p>\n\n\n\n<p>C&#8217;est pour cela que l&#8217;on retourne (<em>k<\/em> &#8211; 1)<em>a<\/em> (pour que le multiple retourn\u00e9 soit inf\u00e9rieur \u00e0 <em>b<\/em>).<\/p>\n\n\n\n<p>Cette derni\u00e8re fonction est bien plus efficace que la premi\u00e8re car il y a bien moins de nombres \u00e0 analyser.<\/p>\n\n\n\n<p>N&#8217;oubliez pas que si vous rencontrez des difficult\u00e9s en math\u00e9matiques, <a href=\"https:\/\/courspasquet.fr\" target=\"_blank\" rel=\"noreferrer noopener\">je peux vous aider par webcam<\/a> !<\/p>\n\n\n\n<p class=\"has-text-align-center\"><a href=\"https:\/\/www.mathweb.fr\/euclide\/ressources-python\/\">[Retour \u00e0 la page des ressources Python]<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Afin de d\u00e9terminer le plus grand multiple d&#8217;un nombre inf\u00e9rieur \u00e0 un autre en Python, il faut savoir comment v\u00e9rifier si deux nombres sont bel et bien multiples. Il faut aussi avoir une id\u00e9e de la fa\u00e7on dont on peut s&#8217;y prendre du point de vue algorithmique. Approche math\u00e9matique pour [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-3196","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Multiple \u00e0 un nombre inf\u00e9rieur \u00e0 un autre en Python - Mathweb.fr<\/title>\n<meta name=\"description\" content=\"D\u00e9terminer le plus grand multiple d&#039;un nombre inf\u00e9rieur \u00e0 un autre en Python : deux m\u00e9thodes (balayage et boucle while). 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