IR-TST 2011 Problem 4

Define a finite set $A$ to be 'good' if it satisfies the following conditions:

• (a) For every three disjoint element of $A,$ like $a,b,c$ we have $\gcd(a,b,c)=1;$
• (b) For every two distinct $b,c\in A,$ there exists an $a\in A,$ distinct from $b,c$ such that $bc$ is divisible by $a.$

Find all good sets.