How many natural numbers less than 600 are neither multiples of 4 nor multiples of 6?

400

Step-by-step explanation:

There are 599 numbers from 1 to 599.

There are

INT (599/4) = 149 numbers divisible by 4 and

INT (599/6) = 99 numbers divisible by 6,

However, some of these numbers have been counted twice. For example, 12 is counted twice, because 12 is divisible by both 4 and 6. There are

INT (599/12) = 49 numbers divisible by 12.

599 numbers

-149 divisible by 4

- 99 divisible by 6

+49 double-counts

400 numbers not divisible by 4 or 6.