Fix integers b>aβ₯1 with g:=gcd(a,b). A set SβN is
\emph{{a,b}-multiplicative} if axξ =by for all x,yβS. For all n,
we determine an {a,b}-multiplicative set with maximum cardinality in [n],
and conclude that the maximum density of an {a,b}-multiplicative set is
b+gbβ. For A,BβN, a set SβN
is \emph{{A,B}-multiplicative} if ax=by implies a=b and x=y for
all aβA and bβB, and x,yβS. For 1<a<b<c and a,b,c
coprime, we give an O(1) time algorithm to approximate the maximum density of
an {{a},{b,c}}-multiplicative set to arbitrary given precision