Given that * is an operation that is valid on the set S = {1,2,3,4,5} defined by a*b = LCM of a and b.

According to the problem it is given that on applying the operation * for two given numbers in the set ‘S’ it gives a number in the set ‘S’ as a result of the operation.

Let us take the values of a = 2 and b = 3.

We know that L.C.M of two prime numbers is given by the product of that two prime numbers.

⇒ L.C.M of a and b is 2×3 = 6.

⇒ 6∉S

∴ The operation * does not define a binary operation on ‘S’.