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If gcd(a,b)=1 then prove that gcd(ac,b)=gcd(c,b)

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HINT: (a,b) = 1 means that there is some x and y such that ax + by = 1
perhaps start by writing \(d=gcd(ac,b)\) and \(e=gcd(b,c)\) and then show that \(d|e\) and \(e|d\)
How about this:

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yes i guess that will do it. notice this fairly obvious fact actually takes a few lines to prove!
Yes, sat, it's one of the many things of number theory which are just intuitively plausible.
what do you mean @FoolForMath
If you see Sivaram's answer, he has used the same fact I alluded to you :)

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