Question: Find the LCM between x² -9, and 3x³ +81.

Solution:
Given,

1st expression: x² -9  = (x+3)(x-3)

2nd expression: 3x³ +81
= 3(x³+27)
= 3(x³ +3³)
= 3(x+3)(x² -3x +3²)
= 3(x+3)(x² -3x +9)

Now,

Lowest Common Multiples (L.C.M.) = common factors * rest factors

= (x+3) * 3(x-3)(x²-3x+9)
= 3 (x+3)(x-3) (x² -3x +9)
= 3(x²-9) (x²-3x+9)



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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