Start summing g+h with g+h. you'll get m(g+h), where m is an integer. since hcf(|g|,|h|)=1, the intersection of <g> and <h> is the {0}. thus, m(g+h)=mg+mh is always different from 0 unless both mg=0 and mh=0. That happens when m=lcm(|g|,|h|)=|g|*|h|.