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Let ∗ be the binary operation on N given by a ∗ b = L.C.M. of a and b. Find

  1. 5 ∗ 7, 20 ∗ 16
  2. Is ∗ commutative?

solution:

(i) 5 ∗ 7 = LCM of 5 and 7 = 35

20 ∗ 16 = LCM of 20 and 16 = 80

(ii) Is ∗ commutative?

a ∗ b = L.C.M. of an and b ∗ a = L.C.M. of b and a ∗ b = b ∗ a

Along these lines ∗ is commutative.