Question

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.

Answer 1

It is given that the operation ∗ on the set A={ 1,2,3,4,5 } is defined as a∗b=LCM( a,b ).

Draw the operation table for the given operation ∗ that is shown below.

∗	1	2	3	4	5
1	1	2	3	4	5
2	2	2	6	4	10
3	3	6	3	12	15
4	4	4	12	4	20
5	5	10	15	20	5

Table (1)

From the binary operation table, it can be observed that the operation ∗ is commutative because 2∗3=3∗2, but the result does not belong to the given domain that is A={ 1,2,3,4,5 }.

Thus, the given operation ∗ is not a binary operation.