Question: Find the LCM between 2x³ +2x² -12x, 6x³ -6x² -72x, and 4x³ -24x² +32x.


Solution:
Given,

1st expression: 2x³ +2x² -12x
= 2x (x² +x -6)
= 2x {x² +(3-2)x -6}
= 2x (x² +3x -2x -6)
= 2x {x(x+3) -2(x+3)}
= 2x (x+3)(x-2)

2nd expression: 6x³ -6x² -72x
= 6x (x² -x -12)
= 6x {x² -(4-3)x -12}
= 6x (x² -4x +3x -12)
= 6x {x(x -4) +3(x -4)}
= 2x * 3x(x +3)(x -4)

3rd expression: 4x³ -24x² +32x
= 4x (x² -6x +8)
= 4x {x² -(4+2)x +8}
= 4x (x² -4x -2x +8)
= 4x {x (x -4) -2 (x -4)}
= 2x * 2x (x -2)(x -4)

Now,

Lowest Common Multiples (L.C.M.) = common factors* rest factors
= 2x (x+3)(x-2)(x -4) * 3x * 2x
= 12x (x-2)(x+3)(x-4)

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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