Discussion
L.C.M. of \((2x^{2}-3xy)^{2}\), \((4x-6y)^{3}\) and \((8x^{3}-27y^{3})\) is ______ ?
Answer: B
Factorise each expression:
\[(2x^{2}-3xy)^{2}=x^{2}(2x-3y)^{2}\]\[(4x-6y)^{3}=2^{3}(2x-3y)^{3}\]\[8x^{3}-27y^{3}=(2x-3y)(4x^{2}+6xy+9y^{2})\]The L.C.M. takes the highest power of each factor: 2 cubed, x squared, (2x-3y) cubed and (4x^2+6xy+9y^2). So the L.C.M. is the expression in option B. Options with lower powers of 2 or of (2x-3y) miss part of (4x-6y) cubed.
The numerical factor 2 to the power 3 comes from (4x - 6y) cubed, because 4x - 6y = 2(2x - 3y), and the power of x comes from x squared in the first expression.
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