How many integers between 1 and 99 inclusive are not divisib

How many integers between 1 and 99, inclusive, are not divisible by either 3 or 7? (This means that they are not divisible by 3 and also they are not divisible by 7.)

Solution

There are 33 multiples of 3 between 1 and 99

There are 14 multiples of 7 between 1 and 99.

Further there are also, 4 multiples of 21. ------> ( 21, 42 , 63, 84)
Total of all above 33 + 14 - 4 = 43, multiples of 3 or 7.    ( subtracting 4 as they are being counted twice)

So, there are 99 - 43 = 56 numbers which are neither divisible by 3 nor by 7