这筐苹果至少有多少个?

  • 时间:2020-04-08 12:54:44
  • 分类:数学世界
  • 阅读:98 次

这仍然是一道剩余定理的问题,剩余定理的解答方法因其较为复杂,过一段时间之后需要温习一下,并试着做一做,不然容易遗忘。题目如下:

一筐苹果4个4个数余1,5个5个数余3,7个7个数余2.这筐苹果至少有多少个?

解答过程:先分别求出4、5、7中每两个数的最小公倍数和这三个数的最小公倍数。

4和5的最小公倍数:4×5=20

5和7的最小公倍数:5×7=35

4和7的最小公倍数:4×7=28

4、5、7的最小公倍数:4×5×7=140。

接着逐个地满足题中的条件:除以4余1的35的倍数是35×3=105;除以5余3的28的倍数就是28;除以7余2的20的倍数是20×5=100,将它们加起来就是:105+28+100=233,再减去它们的最小公倍数得:233-140=93。所以这筐苹果至少有93个。

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