Question

Find the LCM of set of polynomials $x^2-2x,x^2-4$.

Short answer

The LCM of given polynomials is $x\left(x^2-4\right)$.

Step-by-step solution

Step 1. Write down the given polynomials.

The given polynomials are $x^2-2x,x^2-4$.

Step 2. Factorize the polynomials and take common factors of each higher power.

The polynomial $x^2-2x$is factorized as: $\left(x\right)\left(x-2\right)$

The polynomial $x^2-4$is factorized as: $\left(x-2\right)\left(x+2\right)$

Taking common factors of each higher power, the LCM of given polynomials is written as:

$\begin{array}{l}LCM=\left(x\right)\left(x-2\right)\left(x+2\right)\\ =x\left(x^2-4\right)\end{array}$

$\begin{array}{l}LCM=\left(x\right)\left(x-2\right)\left(x+2\right)\\ =x\left(x^2-4\right)\end{array}$

Step 3. Conclusion.

The LCM of given polynomials is $x\left(x^2-4\right)$.