Question

$a$ 和 $b$ 的最小公倍数是 $12$ ， $b$ 和 $c$ 的最小公倍数是 $15$ 。 $a$ 和 $c$ 的最小公倍数的最小可能值是多少？

The least common multiple of $a$ and $b$ is $12,$ and the least common multiple of $b$ and $c$ is $15.$ What is the least possible value of the least common multiple of $a$ and $c?$

$20$

$30$

$60$

$120$

$180$

答案：A

知识点：最小公倍数

难度评级：1390

视频讲解：

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文字解答：

$b$ 必须同时整除 $12$ 和 $15$ ，所以它只能是 $1$ 或 $3$ 。

如果 $b = 1$ ，则可取 $a = 12$ 、 $c = 15$ ，它们的最小公倍数为 $60$ 。如果 $b = 3$ ，则可取 $a = 4$ 、 $c = 5$ ，此时最小公倍数为 $20$ 。

所以正确答案是 A。

We know that $b$ has to divide both $12$ and $15,$ so it must equal either $1$ or $3.$

If $b = 1,$ then $a = 12$ and $c = 15,$ making their least common multiple $60.$ If $b = 3,$ then we may take $a = 4$ and $c = 5.$ The least common multiple in this scenario is $20.$

Thus, A is the correct answer.

2016 AMC 8 第 20 题

答案：A

难度评级：1390

视频讲解：

文字解答：

其他年份的第 20 题