Chapter 4.4, Problem 20WE

(a).

To determine

To find: the GCF of the given monomials.

Answer to Problem 20WE

The GCF of $52r^{2}s$ and $78r{s}^{2}t$ is $26rs$ .

Explanation of Solution

Given information :

The given monomials:

  $52r^{2}s,\text{}78r{s}^{2}t$

Calculation :

The prime factorization of the coefficients are:

  $\begin{array}{l}52=2^2\cdot 13\\ 78=2\cdot 3\cdot 13\end{array}$

The GCF of $52$ and $78$ is

  $2\cdot 13=26$

Compare the powers of each variable occurring in both monomials. Use the power with the least exponent.

Compare $r^2$ and $r$ . Use $r$ .

Compare $s$ and $s^2$ . Use $s$ .

  $\text{GCF}=26\cdot r\cdot s=26rs$

Therefore, the GCF of $52r^{2}s$ and $78r{s}^{2}t$ is $26rs$ .

(b).

To determine

The LCM of the given monomials.

Answer to Problem 20WE

The LCM of $52r^{2}s$ and $78r{s}^{2}t$ is $156r^2{s}^{2}t$ .

Explanation of Solution

Given information :

The given monomials:

  $52r^{2}s,\text{}78r{s}^{2}t$

Calculation :

As per problem,

The prime factorization of the coefficients are:

  $\begin{array}{l}52=2^2\cdot 13\\ 78=2\cdot 3\cdot 13\end{array}$

The LCM of $52$ and $78$ is

  $2^2\cdot 3\cdot 13=156$

Compare the powers of each variable occurring in either monomial. Use the power with the greatest exponent.

Compare $r^2$ and $r$ . Use $r^2$ .

Compare $s$ and $s^2$ . Use $s^2$ .

Use $t$ .

  $\text{LCM}=156\cdot r^2\cdot s^2\cdot t=156r^2{s}^{2}t$

Therefore, the LCM of $52r^{2}s$ and $78r{s}^{2}t$ is $156r^2{s}^{2}t$ .