Question

怎样用短除法求三个数的最小公倍数

Answer 1

例如：求12与18的最大公因数。
12的因数有：1、2、3、4、6、12。
18的因数有：1、2、3、6、9、18。
12与18的公因数有：1、2、3、6。
12与18的最大公因数是6。
这种方法对求两个以上数的最大公因数，特别是数目较大的数，显然是不方便的。于是又采用了给每个数分别分解质因数的方法。
12＝2×2×3
18＝2×3×3
12与18都可以分成几种形式不同的乘积，但分成质因数连乘积就只有以上一种，而且不能再分解了。所分出的质因数无疑都能整除原数，因此这些质因数也都是原数的约数。从分解的结果看，12与18都有公因数2和3，而它们的乘积2×3＝6，就是12与18的最大公因数。
采用分解质因数的方法，也是采用短除的形式，只不过是分别短除，然后再找公因数和最大公因数。如果把这两个数合在一起短除，则更容易。
从短除中不难看出，12与18都有公因数2和3，它们的乘积2×3＝6就是12与18的最大公因数。与前边分别分解质因数相比较，可以发现：不仅结果相同，而且短除法竖式左边就是这两个数的公共质因数，而两个数的最大公因数，就是这两个数的公共质因数的连乘积。
实际应用中，是把需要计算的两个或多个数放置在一起，进行短除，如附图1。
在计算多个数的最小公倍数时，对其中任意两个数存在的因数都要算出，其它无此因数的数则原样落下。最后把所有因数和最终剩下每两个都是互质关系（除1以外没有其他公因数）的数连乘即得到最小公倍数。如图2。

Answer 2

先用三个数的公倍数除，然后再用两个数的公倍数除，除到两两互质为止。最后，把短除号外的所有数都乘起来，就可以得到最小公倍数。这道题比较特殊，因为12和24都是48的因数，所以它们的最小公倍数就是48

Answer 3

举一个例子：60、45、72的最小公倍数是360，用短除法来做就是：
1.同时除以5，得出12.9.72
2.同时除以3 得出4.3.24
3.同时除以2 得出2.3.12
4.同时除以2 得出1.3.6
5.同时除以3 得出1.1.2
60.45.72的最小公倍数=360

Answer 4

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Answer 5

1、先用三个数公有的质因数（或约数）连续去除；
2、当三个数没有公有质因数时，再用其中两个数公有的质因数去除，一直除到最后的三个

商两两互质为止；
3、把所有的除数和最后的商连乘起来。