The only numbers that are divisible by 5 end in either 0 or 5. Numbers where the sum of the digits is divisible by 3 are divisible by 3.
Since the desired number must be strictly greater than 200, then next number that ends in either 0 or 5 is 205. But the sum of the digits of 205 is 7 which is not divisible by 3. The next number that is divisible by 5 is 210. The sum of the digits of 210 is 3 which is divisible by 3, hence 210 is divisible by 5 because it ends in 0 and 210 is divisible by 3 because its sum of digits is divisible by 3. Not only did we find a number >200 divisible by both 3 and 5, but we found the smallest number >200 that is divisible by both 3 and 5.
John
My calculator said it, I believe it, that settles it
