13. How many five-digit numbers are exactly divisible by $6$, $7$, $8$, and $9$?
13.【Solution】The least common multiple of $6, 7, 8, 9$ is 504; among five-digit numbers, the smallest is 10000, and the largest is 99999:
$$
\because \frac{10000}{504}=19 \frac{424}{504}, \frac{99999}{504}=198 \frac{20}{504}
$$
$\therefore$ Among five-digit numbers, those divisible by 504 are $198-19=179$ (numbers)
Answer: There are 179