Let $$ be the binary operation on N given by $a b = L C M$ of a and b.
(i) Find the identity of $*$ in N

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Solution

The binary operation $$ on N is defined as $a b = L C M$ of a and b.
It is known that
LCM of a and 1 =a =LCM of 1 and a, $a \in N .$
$a * 1 = a = 1 * a, a \in N$
Thus, 1 is the identity of $*$ in N.

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