a and b are positive integers such that they do not have any common pr

If a number is divisible by d, say, then the number will also always be divisible by every factor of d. So, for example, if a number is divisible by 12, it must also be divisible by 6, 4, 3 and 2. You can see why by factoring - if a number is divisible by 12, then it equals 12q, where q is a whole number. But then it also equals 6(2q), so it's a multiple of 6 too, for example, and it also equals 4(3q), so it's a multiple of 4, and so on.

So if a number is divisible by 4ab, it is divisible by every divisor of 4ab, so it's divisible by ab, and by 4, and by 4a, and by 2b, and by several other things.

Notice in your example, where a = 3 and b = 5, then ab = 15, and 4ab = 60. That number is not divisible by 16, since 60/16 is not an integer -- it does share some divisors with 16, so you can cancel that fraction down a bit, to 15/4, but you don't get an integer when you're finished canceling.