Prove that if a|c, b|c, (a,b)=d then ab|cd.

Having a little trouble with these kinds of proofs. Help would be greatly appreciated until I wrap my head around them. I figured if you can prove that ab|c that would be all that's required because d has to be an integer. Having said that, I'm having issues proving ab|c, even though it makes sense to me intuitively. 2|16, 4|16 therefore 8|16... but how do you prove that?