Option 1 : 264

First and last number between the given range divisible by ‘3’ is ‘3’ and ‘564’ respectively.

Total numbers between given range that are divisible by ‘3’ = [(564 – 3)/3] + 1 = 188

First and last number between the given range divisible by ‘5’ is ‘5’ and ‘565’ respectively.

Total numbers between given range that are divisible by ‘5’ = [(565 – 5)/5] + 1 = 113

First and last number between the given range divisible by ‘15’ is ‘15’ and ‘555’ respectively.

Total numbers between given range that are divisible by ‘3’ = [(555 – 15)/15] + 1 = 37

Total integers between 1 and 566 are divisible by either 3 or 5 = (188 + 113) – 37 = 264