Question

从 $1$ 到 $46$ 的整数中，有多少个能被 $3$ 或 $5$ 或两者都整除？

How many whole numbers from $1$ through $46$ are divisible by either $3$ or $5$ or both?

$18$

$21$

$24$

$25$

$27$

不超过 $46$ 的 $3$ 的倍数有 $15$ 个， $5$ 的倍数有 $9$ 个。 $15$ 的倍数有 $3$ 个，即 $15$ 、 $30$ 、 $45$ ，它们被重复计算了。

用容斥原理，所求个数是 $15 + 9 - 3 = 21$ 。

所以正确答案是 B。

There are $15$ multiples of $3$ and $9$ multiples of $5$ up to $46.$ The $3$ multiples of $15$ (namely $15,$ $30,$ $45$ ) were counted twice.

By inclusion-exclusion, the count is $15 + 9 - 3 = 21.$

Thus, the correct answer is B .