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(A) The identity element $e$ for a binary operation $^*$ on a set $N$ is an element such that $a \, ^* \, e = a = e \, ^* \, a$ for all $a \in N$. Giv

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$1$

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(A) The identity element $e$ for a binary operation $^*$ on a set $N$ is an element such that $a \, ^* \, e = a = e \, ^* \, a$ for all $a \in N$. Given that $a \, ^* \, b = 	ext{L.C.M. of } a 	ext{ and } b$. We know that the $	ext{L.C.M.}$ of any natural number $a$ and $1$ is $a$,i.e.,$	ext{L.C.M.}(a, 1) = a$ and $	ext{L.C.M.}(1, a) = a$. Therefore,$a \, ^* \, 1 = a = 1 \, ^* \, a$ for all $a \in N$. Thus,$1$ is the identity element of $^*$ in $N$.

Let $^$ be the binary operation on $N$ given by $a \, ^ \, b = \text{L.C.M. of } a \text{ and } b$. Find the identity of $^*$ in $N$.

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Let $^*$ be the binary operation on $N$ given by $a \, ^* \, b = \text{L.C.M. of } a \text{ and } b$. Find the identity of $^*$ in $N$.