* is an operation as m*n = LCM (m, n) where m, n ∈ N. Let m = 2 and b = 3 two natural numbers.

m*n = 2*3

= LCM (2, 3)

= 6∈ N

So, * is a binary operation from .

For commutative,

n*m = 3*2

= LCM (3, 2)

= 6∈ N

Since m*n = n*m, hence * is commutative operation.

Again, for associative, let p = 4

m*(n*p) = 2*LCM (3, 4)

= 2*12

= LCM (2, 12)

= 12∈ N

(m*n) *p = LCM (2, 3) *4

= 6*4

= LCM (6, 4)

= 12∈ N

As m*(n*p) = (m*n) *p, hence * an associative operation.