Is ∗ defined on the set {1, 2, 3, 4, 5} by a ∗ b = L.C.M. of a and b a binary operation? Justify your answer.

The operation * on the set A = {1, 2, 3, 4, 5} is defined as

a * b = LCM of a and b.

2 * 3 = LCM of 2 and 3 = 6.

But 6 does not belong to the given set.

Therefore, the given operation * is not a binary operation.