For how many integers ';a'; between 30 and 40 is it true that 5/a,8/a and 13/a are all in lowest terms?

Essentially you are looking for all integers between 30 and 40 (inclusive?) that are not divisible by 5, 2, or 13. The integers in that range that are divisible by 2, 5, or 13 are 30, 32, 34, 35, 36, 38, 39, and 40. Those that are not are 31, 33, and 37.