Q.6 Let ∗ be the binary operation on N given by a ∗ b = L.C.M. of a and b. Find

(iii) Is ∗ associative?

Answers (1)

a * b = L.C.M. of a and b

(iii)  a,b,c \in N

      (a*b)*c = (L.C.M \, of\, a\, and \, b)*c= L.C.M\, of \, a,b\, and\, c

     a*(b*c) = a*(L.C.M \, of\, b\, and \, c)= L.C.M\, of \, a,b\, and\, c

\therefore \, \, \, \, \, \, \, \, \, (a*b)*c=a*(b*c)

Hence, the operation is associative.

 

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