Question

Is $\ast$ defined on the set $\{1,2,3,4,5\}$ by $a\ast b=L.C.M.$ of $a$ and $ba$ binary operation? Justify your answer

Answer 1

$a\ast b=L.C.M$ of $a$ and $b$.

here $a,bϵ\{1,2,3,4,5\}$

Let $a=2,b=3$

$a\ast b=2\ast 3=LCMof2\&3=6$

Since $6$ is not in set $\{1,2,3,4,5\}$

So $\ast$ is not a binary operation.