Question: Find the L.C.M. between 6x² -x -1 and 54x⁴ +2x.


Solution:
Given,

1st expression: 6x² -x -1
= 6x² -(3-2)x -1
= 6x² -3x +2x -1
= 3x(2x -1) +1(2x -1)
= (3x +1)(2x -1)

2nd expression: 54x⁴ +2x
= 2x (27x³ +1)
= 2x {(3x)³ +(1)³}
= 2x (3x +1)(9x² -3x +1)

Now,

Lowest Common Multiples (L.C.M.) = common factors * rest factors
= (3x +1) * 2x (2x -1)(9x²-3x+1)
= 2x (2x -1) (3x +1)(9x² -3x +1)
= 2x (2x -1)(27x³ +1)

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.

#SciPiPupil