Question

Find the LCM of set of polynomials $16a{b}^3,5b^2{a}^2,20ac$.

Short answer

The LCM of given polynomials is $80a^2{b}^{3}c$.

Step-by-step solution

Step 1. Write down the given polynomials.

The given polynomials are $16a{b}^3,5b^2{a}^2,20ac$.

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

The polynomial $16a{b}^3$ is factorized as: $\left(2^4\right)\left(a\right)\left(b^3\right)$

The polynomial $5b^2{a}^2$ is factorized as: $\left(5\right)\left(b^2\right)\left(a^2\right)$

The polynomial $20ac$ is factorized as: $\left(2^2\right)\left(5\right)\left(a\right)\left(c\right)$

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

$\begin{array}{l}LCM=\left(2^4\right)\left(a^2\right)\left(b^3\right)\left(5\right)\left(c\right)\\ =80a^2{b}^{3}c\end{array}$

Step 3. Conclusion.

The LCM of given polynomials is $80a^2{b}^{3}c$.