Answer :
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
perhaps start by writing d=gcd(ac,b) and e=gcd(b,c) and then show that d|e and e|d