How many natural numbers between 43 and 274 are relatively prime to 15? And how could you determine how many natural numbers were relatively prime to 15 between any pair of natural numbers, a and b?

There are 230 natural numbers between 43 and 274 (I assumed this to mean not inclusive). 77 are divisible by 3, 46 are divisible by 5, but 18 are divisible by both 3 and 5. 230 - 77 - 46 + 18 = 125. If you assume INCLUSIVE of 43 and 274, both are relatively prime to 15, so it would be 127.