Q15. - Algebra 2

Question

Find the LCM of set of polynomials $36x^{2}y,20xyz$.

Step-by-Step Solution

Answer

The LCM of given polynomials is $180x^{2}yz$.

Step 1. Write down the given polynomials.

The given polynomials are $36x^{2}y,20xyz$.

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

The polynomial $36x^{2}y$ is factorized as: $\left(2^2\right)\left(3^2\right)\left(x^2\right)\left(y\right)$

The polynomial $20xyz$ is factorized as: $\left(2^2\right)\left(5\right)\left(x\right)\left(y\right)\left(z\right)$

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

$\begin{array}{l}LCM=\left(2^2\right)\left(3^2\right)\left(x^2\right)\left(y\right)\left(5\right)\left(z\right)\\ =180x^{2}yz\end{array}$

Step 3. Conclusion.

The LCM of given polynomials is $180x^{2}yz$.