Q17. - Algebra 2

Question

Find the LCM of set of polynomials $9p^2{q}^3,6p{q}^4,4p^3$.

Step-by-Step Solution

Answer

The LCM of given polynomials is $36p^3{q}^4$.

Step 1. Write down the given polynomials.

The given polynomials are $9p^2{q}^3,6p{q}^4,4p^3$.

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

The polynomial $9p^2{q}^3$ is factorized as: $\left(3^2\right)\left(p^2\right)\left(q^3\right)$

The polynomial $6p{q}^4$ is factorized as: $\left(2\right)\left(3\right)\left(p\right)\left(q^4\right)$

The polynomial $4p^3$ is factorized as: $\left(2^2\right)\left(p^3\right)$

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

$\begin{array}{l}LCM=\left(3^2\right)\left(p^3\right)\left(q^4\right)\left(2^2\right)\\ =36p^3{q}^4\end{array}$

Step 3. Conclusion.

The LCM of given polynomials is $36p^3{q}^4$.