Question

Let $\ast$ be the binary operation on $N$ given by $a\ast b=L.C.M$ of $a$ and $b$. Find
(i) $5\ast 7,20\ast 16$ (ii) Is $\ast$ commutative?

iii) Is $\ast$ associative?

Answer 1

i) Now $5\ast 7=$ LCM of $5$ and $7$$=35$ again $20\ast 16=$ LCM of $20$ and $16$$=80$.

ii) Yes $\ast$ is commutative, because $a\ast b=$ LCM of $a$ and $b=$ LCM of $b$ and $a=b\ast a\forall a,b\in N$.

iii) Yes $\ast$ is also associative, because $a\ast (b\ast c)=$ LCM of $a,b,c=(a\ast b)\ast c$ for $a,b,c\in N$.