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Question
Find the L.C.M. of the given expressions
(2x2 – 3xy)2, (4x – 6y)3, (8x3 – 27y3)
Solution
(2x2 – 3xy)2 = x2 (2x – 3y)2
(4x – 6y)3 = 23 (2x – 3y)3
= 8 (2x – 3y)3
(8x3 – 27y3) = (2x)3 – (3y)3
= (2x – 3y) [(2x)2 + 2x × 3y + (3y2)] ...[using a3 – b3 = (a – b) (a2 + ab + b2)]
(2x – 3y) (4x2 + 6xy + 9y2)
L.C.M. = 8x2 (2x – 3y)3 (4x2 + 6xy + 9y)2
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