Of the numbers 1, 2, 3, . . . , 6000, how many are not multiples of 2, 3 or 5?

My answers is:

3000 multiples of 2, 2000 multiples of 3, 1200 multiples of 5, 600 of 10, 1000 of 6, 400 of 15

So 4200 multiples, by adding the first 3 and subtracting the next 3 from the sum, since they have been counted twice.

So 6000 - 4200 = 1800.

Is this correct?