Chapter 4.4, Problem 19OE

To determine

To find : the GCF and LCM of the given monomials.

Answer to Problem 19OE

For the given monomials, the GCF is $2st$ and LCM is $12r{s}^2{t}^2$ .

Explanation of Solution

Given information :

The given monomials:

  $4s{t}^2\text{ and }6r{s}^{2}t$

Calculation :

As per problem,

The prime factorization of the coefficients are:

  $\begin{array}{l}4=2^2\\ 6=2\cdot 3\end{array}$

1. To find GCF:

The GCF of $4$ and $6$ is $2$ .

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

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

Compare $t^2$ and $t$ . Use $t$ .

$\text{GCF}=2\cdot s\cdot t=2st$

2. To find LCM:

The LCM of $4$ and $6$ is

$2^2\cdot 3=12$

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

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

Compare $t^2$ and $t$ . Use $t^2$ .

Use $w$ .

  $\text{LCM}=12\cdot r\cdot s^2\cdot t^2=12r{s}^2{t}^2$

Therefore, for the given monomials, the GCF is $2st$ and LCM is $12r{s}^2{t}^2$ .