What methods are there to find integers from given GCDs? I need to find the natural numbers a, b, c that satisfy gcd(a,b)=21, gcd(b,c)=21, and gcd(a,c)=819.
I managed to find a set {a=819,b=462,c=819} by some guessing and checking with Mathematica, but I need to be able to do this by hand. I had hoped to reverse engineer some method with a solution and the GCD properties, but so far I'm not having much success. Any help appreciated, thanks.