Chapter 4.5, Problem 8MRE

a.

To determine

To find the GCF of the monomials.

Answer to Problem 8MRE

The value of GCF is $15a^2{b}^3$ .

Explanation of Solution

Given information:

  $30a^2{b}^4,75a^3{b}^3$

Calculation:

The monomial can be obtained as

The prime factorization of the coefficients are

  $\begin{array}{l}30=2\times 3\times 5\text{ and}\\ \text{75=3}\times {\text{5}}^2\end{array}$

The GCF of $30\text{ and 75 is }$

  $\begin{array}{l}3\times 5=15\left[\begin{array}{l}\text{compare the powers of each variable occuring in both monomials}\text{.}\\ \text{use the power with the least component }\end{array}\right]\\ \text{compare }{a}^2{\text{ and a}}^3.\text{ use }{a}^2\\ {\text{compare b}}^4{\text{ and b}}^3.{\text{ use b}}^3\end{array}$

Therefore,

  $GCF=15a^2{b}^3$

Hence,

The value of GCFis $15a^2{b}^3$ .

b.

To determine

To find the LCM of the monomials.

Answer to Problem 8MRE

The value of LCM is $150a^3{b}^4$ .

Explanation of Solution

Given information:

  $30a^2{b}^4,75a^3{b}^3$

Calculation:

The monomial can be obtained as

The prime factorization of the coefficients are

  $\begin{array}{l}30=2\times 3\times 5\text{ and}\\ \text{75=3}\times {\text{5}}^2\end{array}$

The LCM of $\text{30 and 75}$ is

  $\begin{array}{l}2\times 3\times 5^2=150\left[\begin{array}{l}\text{compare the powers of each variable occuring in either monomial}\text{.}\\ \text{use the power with the greatest component }\end{array}\right]\\ \text{compare }{a}^2{\text{ and a}}^3.\text{ use }{a}^3\\ {\text{compare b}}^4{\text{ and b}}^3.{\text{ use b}}^4\end{array}$

Therefore,

  $LCM=150a^3{b}^4$

Hence,

The value of LCMis $150a^3{b}^4$ .