No! You have counted twice the numbers which are multiples of 2,3 and 5. So you should subtract 200 from your result.

One way to do it is to consider the intersection of the set of number which are not multiples of 2, the set of number which are not multiples of 3 and the set of number which are not multiples of 5.

So you would get . If you expand the product you get :

which is consistent with your approach by the inclusion/exclusion principle (once your small mistake is corrected).

Draw a Venn diagram, it might help you understand.