Chapter 4.5, Problem 9MRE

a.

To determine

To find the GCF of the monomials.

Answer to Problem 9MRE

The value of GCF is $21m{p}^2$ .

Explanation of Solution

Given information:

  $63m{p}^2,42m{p}^3$

Calculation:

The monomial can be obtained as

The prime factorization of the coefficients are

  $\begin{array}{l}63=3^2\times 7\text{ and}\\ \text{42=2}\times \text{3}\times 7\end{array}$

The GCF of $\text{63 and 42 is }$

  $\begin{array}{l}3\times 7=21\left[\begin{array}{l}\text{compare the powers of each variable occuring in both monomials}\text{.}\\ \text{use the power with the least component }\end{array}\right]\\ \text{compare }m\text{ and }m.\text{ use }m\\ \text{compare }{p}^2\text{ and }{p}^3.\text{ use }{p}^2\end{array}$

Therefore,

  $GCF=21m{p}^2$

Hence,

The value of GCFis $21m{p}^2$ .

b.

To determine

To find the LCM of the monomials.

Answer to Problem 9MRE

The value of LCM is $126m{p}^3$ .

Explanation of Solution

Given information:

  $63m{p}^2,42m{p}^3$

Calculation:

The monomial can be obtained as

The prime factorization of the coefficients are

  $\begin{array}{l}63=3^2\times 7\text{ and}\\ \text{42=2}\times \text{3}\times 7\end{array}$

The LCM of $\text{63 and 42}$ is

  $\begin{array}{l}2\times 3^2\times 7=126\left[\begin{array}{l}\text{compare the powers of each variable occuring in either monomial}\text{.}\\ \text{use the power with the greatest component }\end{array}\right]\\ \text{compare }m\text{ and }m.\text{ use }m\\ \text{compare }{p}^2\text{ and }{p}^3.\text{ use }{p}^3\end{array}$

Therefore,

  $LCM=126m{p}^3$

Hence,

The value of LCMis $126m{p}^3$ .