# Let $\ast$ be the binary operation on $N$ given by $a \ast b =$ LCM of $a$ and $b$. $(iv)$ Find the identity of $\ast$ in $N$.

$\begin{array}{1 1} 0 \\ 1 \\ a \ast b\\ LCM*(a,b)\end{array}$

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.
Given that the binary operation on N given by $a \ast b =$ LCM $(a,b)$:
To find the identity of $\ast$, we take the LCM $(a,1)$ and LCM $(1,a)$:
LCM $(a,1) = a$ and LCM $(1,a) = a \rightarrow 1$ is the identity of $\ast$ in $N$.