Find the least common multiple of the following pair of

Find the least common multiple of the following pair of polynomials:
$x{\left(x-1\right)}^{2}\left(x+1\right)$ and $4\left(x-1\right){\left(x+1\right)}^{3}$
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Thomas Nickerson
Step 1
The least common multiple (LCM) is the smallest quantity which is multiple of more than one quantity. To find the LCM of two polynomials, we have to perform the following process.
Factors each polynomial
Take out the common factors of both polynomials
Multiply the remaining uncommon factors
Multiply the common and uncommon factors to each other to find the LCM.
Step 2
The given polynomials already have the factors. So take the common factors of polynomials $x{\left(x-1\right)}^{2}\left(x+1\right)$ and $4\left(x-1\right){\left(x+1\right)}^{3}$. The common factors are x−1 and x+1.
The remaining uncommon factors are x(x−1) and $4{\left(x+1\right)}^{2}$. The product of these factors is $4x\left(x-1\right){\left(x+1\right)}^{2}$. Now, multiply $4x\left(x-1\right){\left(x+1\right)}^{2}$ with common factors to obtain the LCM of both polynomials.
$LCM=4x\left(x-1\right){\left(x+1\right)}^{2}\left(x-1\right)\left(x+1\right)$
$=4x{\left(x-1\right)}^{2}{\left(x+1\right)}^{3}$
Hence, the least common multiple of the given polynomials is $4x{\left(x-1\right)}^{2}{\left(x+1\right)}^{3}$.