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# Let star be the binary operation on N given by a star b equal to L.C.M. of a and b Find Is star associative?

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

(iii) Is ∗ associative?

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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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