Find the LCM of the following
(i) x3 y2 , xyz
(ii) 3x2yz, 4x3 y3
(iii) a2bc, b2ca , c2a b
(iv) 66 a4b2c3 , 44 a3b4c2 , 24 a2b3c4
(v) a(m+1), a(m+2), a(m+3)
(vi) x2y+xy2, x2+xy
(i) Solution :
x3 y2 = x ⋅ x ⋅ x ⋅ y ⋅ y
xyz = x ⋅ y ⋅ z
Comparing x terms (LCM) is x3
Comparing y terms (LCM) is y2
So, the required LCM is x3 y2 z.
(ii) Solution :
3x2yz, 4x3 y3
3x2yz = 3 ⋅ x ⋅ x ⋅ y ⋅ z
4x3 y3 = 4 ⋅ x ⋅ x ⋅ x ⋅ y ⋅ y⋅ y
Comparing x terms (LCM) is x3
Comparing y terms (LCM) is y3
So, the required LCM is 12x3 y3z.
(iii) Solution :
a2bc, b2ca , c2a b
By comparing the given terms, the least common multiple is
a2 b2c2
(iv) Solution :
66 a4b2c3, 44 a3b4c2, 24 a2b3c4
66 = 2⋅3⋅11
44 = 22⋅11
24 = 23⋅3
Highest common factor of 66, 44 and 24 is 23 ⋅ 11 ⋅ 3
= 264
Highest common factor of a4b2c3, a3b4c2 and a2b3c4
= a4b4c4
So, the required LCM is 264a4b4c4.
(v) Solution :
a(m+1), a(m+2), a(m+3)
a(m+1) = am ⋅ a
a(m+2) = am ⋅ a2
a(m+3) = am ⋅ a3
We find am in common for all and highest "a" term is a3.
= am⋅ a3
= a(m+3)
So, the required LCM is a(m+3).
(vi) Solution :
x2y+xy2, x2+xy
x2y+xy2 = xy(x+y)
x2+xy = x(x + y)
By comparing the factors, the least common multiple is
xy(x+y)
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