Help with a divisibility proof

**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?

Re: Help with a divisibility proof

Re: Help with a divisibility proof

Thanks for the help! Your proof makes sense, except for this little bit:

Quote:

Originally Posted by

**TheEmptySet** If we multiply the LCM by 3 we get

You say multiply by three but that doesn't appear in the proof.

EDIT: Wow, I realised what you meant as soon as I posted the reply. LCM being c, and 3 being the third equation. Perfect. Thanks again!