Answer:
Given a * b = L.C.M. of
a and b
(i) 5 * 7 =
L.C.M. of 5 and 7 = 35
20 * 16 = L.C.M.
of 20 and 16 = 80
(ii) a * b = L.C.M.
of a and b
= L.C.M. of b
and a
= b * a
Yes, * is
commutative.
(iii) a * (b * c) =
a* (L.C.M. of b and c)
= L.C.M. of a, b
and c
= (L.C.M. of a
and b) * c
= (a * b) * c
= (a * b) * c
Yes, * is
associative.
(iv) Let e be the identity
element of in N
of a and e =
is the
identify element.
(v) Let ?b? be the
invertible element in N
= 1 (identity
element)
L.C.M. of a
and b ? 1
a = b = 1
is an
invertible element in N.
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