Question

Find the LCM of set of polynomials $10s^2,35s^2{t}^2$.

Short answer

The LCM of given polynomials is $70s^2{t}^2$.

Step-by-step solution

Step 1. Write down the given polynomials.

The given polynomials are $10s^2,35s^2{t}^2$.

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

The polynomial $10s^2$ is factorized as: $\left(2\right)\left(5\right)\left(s^2\right)$

The polynomial $35s^2{t}^2$ is factorized as: $\left(5\right)\left(7\right)\left(s^2\right)\left(t^2\right)$

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

$\begin{array}{l}LCM=\left(2\right)\left(5\right)\left(s^2\right)\left(7\right)\left(t^2\right)\\ =70s^2{t}^2\end{array}$

Step 3. Conclusion.

The LCM of given polynomials is $70s^2{t}^2$.