Question: Find the LCM between x³ -9x, x⁴ -2x³ -3x², and x³ -27.


Solution:
Given,

1st expression: x³ -9x
= x(x²-9)
= x(x² -3²)
= x(x+3)(x-3)

2nd expression: x⁴ -2x³ -3x²
= x²(x² -2x -3)
= x²{x² -(3-1)x -3}
= x²(x² -3x +x -3)
= x²{ x(x-3) + 1(x-3)}
= x² (x+1)(x-3)

3rd expression: x³ -27
= (x³ -3³)
= (x -3)(x² +3x +9)

Now,

Lowest Common Multiples (L.C.M.) = common factors* rest factors
= x(x-3) * x(x+3)(x+1)(x²+3x+9)
= x*x (x+1) (x+3) (x-3)(x²+3x+9)
= x² (x+1) (x-3) (x³-27)

Related Notes and Solutions:

Here is the Website link to the guide of solving HCF and LCM.
Here are all solutions of LCM for Class 10.

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