Question

Let $\ast$ be the binary operation on $N$ given by $a\ast b=$ LCM of $a$ and $b$. Find
Find the identify of $\ast$ in $N$

Answer 1

Let ${}^{\prime }{e}^{\prime }$ be the identity element, than
$a\ast e=e\ast a=a\forall aϵN$
$L.C.M.(a,e)=L.C.M.(e,a)=a$
$\Rightarrow e$ divides $a\forall aϵN$
$\Rightarrow e=1$
$\therefore 1$ is the identity element.