Question

Find the LCM of set of polynomials $14a^3,15b{c}^3,12b^3$.

Short answer

The LCM of given polynomials is $420a^3{b}^3{c}^3$.

Step-by-step solution

Step 1. Write down the given polynomials.

The given polynomials are $14a^3,15b{c}^3,12b^3$.

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

The polynomial $14a^3$ is factorized as: $\left(2\right)\left(7\right)\left(a^3\right)$

The polynomial $15b{c}^3$ is factorized as: $\left(3\right)\left(5\right)\left(b\right)\left(c^3\right)$

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

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

$\begin{array}{l}LCM={\left(2\right)}^2\left(7\right)\left(a^3\right)\left(3\right)\left(5\right)\left(b^3\right)\left(c^3\right)\\ =420a^3{b}^3{c}^3\end{array}$

Step 3. Conclusion.

The LCM of given polynomials is $420a^3{b}^3{c}^3$.