# Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(ii)$ Is $\ast$ commutative?

This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com

Toolbox:
• The lowest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b.
• An operation $\ast$ on $A$ is commutative if $a\ast b = b \ast a\; \forall \; a, b \in A$
Given that the binary operation on N given by $a \ast b =$ LCM $(a,b)$:
We know from the definition of LCM that LCM $(a,b)$ = LCM $(b,a)$. Therefore, $\ast$ is commutative.
answered Mar 19, 2013