Question

Let * be the binary operation on N given by a * b = L.C.M. of a and b. Find

(i) 5 * 7, 20 * 16               (ii) Is * commutative?
(iii) Is * associative?        (iv) Find the identity of * in N
(v) Which elements of N are invertible for the operation *?

Answer 1

The binary operation * on N is defined as a * b = L.C.M. of a and b.
(i) 5 * 7 = L.C.M. of 5 and 7 = 35
20 * 16 = L.C.M of 20 and 16 = 80

This case is possible only when a and b are equal to 1. Thus, 1 is the only invertible element of N with respect to the operation *.