1. The number of natural numbers less than 1000 that are neither divisible by 5 nor by 7 is ().
(A) 658
(B) 648
(C) 686
(D) 688
,$- 1 . C$.
Among the 999 natural numbers less than 1000, there are $\left[\frac{999}{5}\right]$ numbers divisible by 5, $\left[\frac{999}{7}\right]$ numbers divisible by 7, and among them, $\left[\frac{999}{5 \times 7}\right]$ numbers are divisible by both 5 and 7. Therefore, the number we are looking for is:
$$
999-\left(\left[\frac{999}{5}\right]+\left[\frac{999}{7}\right]-\left[\frac{999}{5 \times 7}\right]\right)=686 .
$$