仅由 0/1 组成的最小 15 的倍数

要被 15 整除需同时被 3 与 5 整除。

• 被 5 整除：末位必须为 0（因为不能出现 5）。
• 被 3 整除：各位数字和必须是 3 的倍数。因为只含 0/1，所以等价于“1 的个数是 3 的倍数”。

最小满足条件的数为 $1110$。

---

Original Explanation

In order for a number to be a multiple of 15, it must be perfectly divisible by both 3 and 5. In order for the number to be divisible by 5, it must end in either a 0 or 5—thus, our number must end in a 0. In order for the number to be divisible by 3, the sum of its digits must be a multiple of 3—thus, we will add three 1's digits to the number. Hence, the smallest positive multiple of 15 whose digits consist of 1's and 0's only is 1110.