Question

Lcm is 360 then then how many pairs are possible

Answer 1

Because 300=22×3×52300=22×3×52, we can say that
A=2a13a25a3A=2a13a25a3
B=2b13b25b3B=2b13b25b3
with the conditions that
max(a1,b1)=2(a1,b1)=2; max(a2,b2)=1(a2,b2)=1; max(a3,b3)=2(a3,b3)=2

This gives us 5 options for (a1,b1)(a1,b1); 3 for (a2,b2)(a2,b2) and 5 for (a3,b3)(a3,b3). Hence there are 75 pairs of A, B. But we want the number of sets. Everything other than 300, 300 comes twice. So the final answer is 38.