10. (3 points) The sum of all natural numbers between 1 and 200 that are not multiples of 2 or 5 is
10. (3 points) The sum of all natural numbers between $1 \sim 200$ that are not multiples of 2 or 5 is 8000.
【Solution】: The sum of all natural numbers from 1 to 200 is: $1+2+3+\cdots+200=20100$,
The sum of all natural numbers that are multiples of 2 from 1 to 200 is:
$$
2+4+6+8+\cdots+198+200=2 \times(1+2+3+\cdots+100)=2 \times 5050=10100,
$$
The sum of all natural numbers that are multiples of 5 from 1 to 200 is:
$$
5+10+15+20+\cdots+195+200=5 \times(1+2+3+\cdots+40)=5 \times 820=4100,
$$
The sum of all natural numbers that are multiples of both 2 and 5 from 1 to 200 is:
$$
10+20+30+\cdots+200=10 \times(1+2+3+\cdots+20)=10 \times 210=2100,
$$

Therefore, the sum of all natural numbers from 1 to 200 that are not multiples of 2 or 5 is:
$$
S=20100-10100-4100+2100=8000 ;
$$

The answer is: 8000 .