8 和 18 的最小公倍数是多少?
最小公倍数(Least Common Multiple,简称 LCM)是指两个或多个数共同拥有的倍数中最小的一个数。对于 8 和 18,它们的倍数如下:
8 的倍数:8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144,152,160,168,176,184,192,200,208,216,224,232,240,248,256,264,272,280,288,296,304,312,320,328,336,344,352,360,368,376,384,392,400,408,416,424,432,440,448,456,464,472,480,488,496,504,512,520,528,536,544,552,560,568,576,584,592,600,608,616,624,632,640,648,656,664,672,680,688,696,704,712,720,728,736,744,752,760,768,776,784,792,800,808,816,824,832,840,848,856,864,872,880,888,896,904,912,920,928,936,944,952,960,968,976,984,992,1000,...
18 的倍数:18,36,54,72,90,108,126,144,162,180,198,216,234,252,270,288,306,324,342,360,378,396,414,432,450,468,486,504,522,540,558,576,594,612,630,648,666,684,702,720,738,756,774,792,810,828,846,864,882,900,918,936,954,972,990,1008,...
可以看到,两个数的公共倍数包括:72,144,216,288,360,432,504,576,648,720,792,864,936,1008,...
其中最小的数为 72,因此 8 和 18 的最小公倍数为 72。
另外,我们还可以使用下面的方法来求最小公倍数:
- 将两个数分解质因数
8 = 2 * 2 * 2
18 = 2 * 3 * 3
- 将它们的质因数分解写在一起,取每个质因数的最高次幂
2^3 * 3^2 = 72
因此,8 和 18 的最小公倍数为 72。
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