How do I find the Least Common multiple between these

Question

Any help will be greatly appreciated!

Answer 1

lcm CAN BE thought in polynomials as you have to give that polynomial which would when divided by these numbers gives a polynomial as it happens for integers.

So thinking along that line a polynomial I would come across that suffice this condition is

{x+a}x{x-a}

Now I can go to it by just seeing a particular pattern as it happens while dealing with LCM in arithmetic

It will be first take out the factors of each polynomial .

Now take the highest power of each factor that are present in all the polynomials

Here, you see the first polynomial and divide into its factors x+a and x-a now see are these factors available elsewhere and select the highest power of that factor.

Why this magic work?

try to think , If unable comment.