Question

Find the LCM of set of polynomials $4w-12,2w-6$.

Short answer

The LCM of given polynomials is $4\left(w-3\right)$.

Step-by-step solution

Step 1. Write down the given polynomials.

The given polynomials are $4w-12,2w-6$.

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

The polynomial $4w-12$ is factorized as: $\left(2^2\right)\left(w-3\right)$

The polynomial $2w-6$ is factorized as: $2\left(w-3\right)$

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

$\begin{array}{l}LCM=\left(2^2\right)\left(w-3\right)\\ =4\left(w-3\right)\end{array}$

Step 3. Conclusion.

The LCM of given polynomials is $4\left(w-3\right)$.