Question: Find the LCM between a⁴+a²+1, a³-1, and a³-a²+a.


Solution:
Given,

1st expression: a⁴+a²+1
= (a⁴ +1) +a²
= {(a²)² +1²} +a²
= (a²+1)² -2a² +a²
= (a² +1)² - (a)²
= (a² -a +1) (a² +a +1)

2nd expression: a³ -1
= a³ -1³
= (a-1)(a² +a +1)

3rd expression: a³ -a² +a
= a(a² -a +1)

Now,

Lowest Common Multiples (L.C.M.) = common factors * rest factors
= (a² +a +1)(a² -a +1) * a (a -1)
= a *(a-1)* (a²+a+1)(a²-a+1)
= a (a -1)(a⁴ +a² +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