The sum of all natural numbers less than 200, that are  divisible neither by 3 nor by 5, is

The required sum.

$=(1+2+3+\dots +199)-(3+6+9+\dots +198)$$-(5+10+15+\dots +195)+(15+30+45+$$\dots +195)$

$=\frac{199}{2}(1+199)-\frac{66}{2}(3+198)-\frac{39}{2}(5+195)$$+\frac{13}{2}(15+195)$

$=199\times 100-33\times 201-39\times 100+13\times 105$

$=10732$