Question

Find the LCM of set of polynomials $12y^2,6x^2$.

Short answer

The LCM of given polynomials is $12x^2{y}^2$.

Step-by-step solution

Step 1. Write down the given polynomials.

The given polynomials are $12y^2,6x^2$.

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

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

The polynomial $6x^2$ is factorized as: $\left(2\right)\left(3\right)\left(x^2\right)$

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

$\begin{array}{l}LCM=\left(2^2\right)\left(3\right)\left(y^2\right)\left(x^2\right)\\ =12x^2{y}^2\end{array}$

Step 3. Conclusion.

The LCM of given polynomials is $12x^2{y}^2$.