SOLUTION :
$\begin{array}{l}\because a{ }^* b=\operatorname{LCM} \text { of } a \text { and } b=\operatorname{LCM}(a, b) \\\therefore 20^* 16=\operatorname{LCM}(20,16)=80\end{array}$
(i) Let $a, b \in N$
$\therefore a^* b=\operatorname{LCM}(a, b)=\operatorname{LCM}(b, a)=b \text { * } a$
Hence * is commutative.
(ii) Let $a, b, c \in N$
$\begin{array}{l}\therefore\left(a^* b\right)^* c=\operatorname{LCM}(a, b){ }^* c=\operatorname{LCM}(a, b, c) \\\text { and } a^*\left(b^* c\right)=a^* \operatorname{LCM}(b, c)=\operatorname{LCM}(a, b, c) \\\therefore\left(a^* b\right)^* c=a^*\left(b^* c\right)\end{array}$
Hence * is associative.
