fundamental - divisibility

[aimster7888]

I thought I read somewhere that if a number n is divisible by x and it's also divisible by y then it's also divisible by xy. But apparently this is not the case, consider x=12, y=9, xy=108
but n=72 is div by 12 and 9, but clearly not div by 108

The above rule works for some numbers, for example x=3 and y=2 (this is how to test divisibility by 6). Is there a better way to generalize above rule? What's the correct rule?

[bkparikh]

Here's my cut at a generalization:

A number that's divisible by x and by y is divisible by the least common multiple of x and y. In the example, the LCM of 9 and 12 is 36. 108 is divisible by 36.

If the LCM of x and y = x*y then the number will be divisible by x*y (as in the case of 2 and 3).

[abhishek_mumbai]

bkparikh is correct..

and your rule also stands correct if x and y are co-primes.. e.g. 14 and 15 are not prime number but they are co-primes and this rule stand correct for them..