Is * defined on the set {1,2,3,4,5} by a*b = l.c.m. of a and b binary operation?

Question

Is * defined on the set $\{1,2,3,4,5\}$ by $a$ * $b=$ I.c.m. of a and b binary operation?

Answer 1

SOLUTION : $\quad a^* b=\text { l.c.m. of } a \text { and } b $

$\therefore \quad 2{ }^* 3=\text { I.c.m. of } 2 \text { and } 3 $

$\quad=6$

${[\because \text { l.c.m. of } 2 \text { and } 3=2 \times 3=6]}$

$\text { By } \quad 6 \notin\{1,2,3,4,5\}$

$\text { Hence * is not a binary operation on }\{1,2,3,4, 5\}$