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【320564】【详解】5年级第15讲_公约数与公倍数进阶

时间:2025-01-08 18:26:24 作者: 字数:2757字
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第十五讲 公约数与公倍数进阶


  1. 答案:(15472;(2181080722705436090216
    详解:(1)设两个自然数分别是18a18b,那么ab互质.这两个自然数的最小公倍数是18ab,那么有 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> .考虑到这两个数不成倍数关系,ab应该是34,两个自然数分别是5472.(2)设这两个自然数分别是18a18b,然后按照第(1)中的方法来做即可.

  2. 答案:3952
    详解:设这两个自然数分别是13a13b,那么有 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> .可解出ab应该是34,两个自然数分别是3952

  3. 答案:42
    详解:设这两个自然数分别是6a6b,那么有 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> (不妨设ab大).可解出 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> ,较小的数是42

  4. 答案:18
    详解: <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> .首先可知这三个数的质因数只有2357.而且甲中没有7,没有5;乙中没有2,没有73最多有1个;丙中没有2,没有53最多有1个.因为甲、乙的最小公倍数是90,而乙中没有2,最多有13,可以判断出甲中有1223,甲是18

  5. 答案:101
    详解:这四个数的和一定是它们最大公约数的倍数.那么它们的最大公约数一定是1111的约数,可能是1111011001.又因为这四个数两两不同,它们的和至少是最大公约数的 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> 倍.最大公约数最大是101

  6. 答案:204
    详解:最大公约数是12,则两数中质因数23的最低次方分别为21,又因为两数有12的约数,利用约数个数反求法可得两数分解质因数形式为 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a>

  1. 答案:(11627;(2180225
    详解:(1)可知两数乘积是432,只能是1627;(2)设两个自然数分别是45a45b,然后列方程即可.

  2. 答案:648
    详解:设这两个数分别是6a6b,然后列方程即可.

  3. 答案:30
    详解:设两个数分别是10a10b,然后列方程即可.

  4. 答案:7
    详解:参考例题4



  1. 答案:32
    简答:乙数为 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a>

  2. 答案:1220
    简答:最大公约数是 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> .然后设两个数为4a4b求解即可.

  3. 答案:2456
    简答:设两个数分别为8a8b,则有 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> .又因为这两个数不成倍数关系,只能是2456

  4. 答案:15
    简答:要使3个数都不一样,那么它们的和至少是最大公约数的 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> 倍,而 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> ,最大公约数最大只能是15


  5. 答案:12
    简答:甲、乙两数的最小公倍数是 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> ,乙、丙两数的最小公倍数是 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> ,甲、丙两数的最小公倍数是 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a> .对比三个条件,可知甲数为 <a href="/tags/393/" title="公约数" class="c1" target="_blank">公约数</a> <a href="/tags/394/" title="公倍数" class="c1" target="_blank">公倍数</a> <a href="/tags/390/" title="倍数" class="c1" target="_blank">倍数</a> <a href="/tags/392/" title="约数" class="c1" target="_blank">约数</a> <a href="/tags/1312/" title="公约" class="c1" target="_blank">公约</a>

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