Let $$ be the binary operation on N given by $a b = L C M$ of a and b.
(i) Is $*$ associative?

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Solution

The binary operation $$ on N is defined as $a b = L C M$ of a and b.
For $a, b, c \in N$ , we have
$(a * b) * c$ =(LCM of a and b) $* c$ = LCM of a,b, and c

$a * (b * c) = a $ (LCM of b and c) = LCM of a,b and c
$a (b * c) = a * (b * c)$ . Thus, the operation $*$ is associative.

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