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

Q. 7 Is ∗ defined on the set $\{1, 2, 3, 4, 5\}$ by $a * b = L.C.M. \;of \;a\; and \;b$ a binary

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$a * b = L.C.M. \;of \;a\; and \;b$

A = $\{1, 2, 3, 4, 5\}$

Operation table is as shown below:

 $*$ 1 2 3 4 5 1 1 2 3 4 5 2 2 2 6 4 10 3 3 6 3 12 15 4 4 4 12 4 20 5 5 10 15 20 5

From the table, we can observe that

$2*3=3*2=6 \notin A$

$2*5=5*2=10 \notin A$

$3*4=4*3=12 \notin A$

$3*5=5*3=15 \notin A$

$4*5=5*4=20 \notin A$

Hence, the operation is not a binary operation.

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