Chapter 4.4, Problem 22OE

To determine

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

Answer to Problem 22OE

For the given monomials, the GCF is $a{r}^2$ and LCM is $24a^2{r}^3{s}^3$ .

Explanation of Solution

Given information :

The given monomials:

  $12a{r}^2{s}^3,8a^2{r}^{2}s,\text{ and }a{r}^3$ .

Calculation :

As per problem,

The prime factorization of the coefficients are:

  $\begin{array}{l}12=2^2\cdot 3\\ 8=2^3\end{array}$

The coefficient of $a{r}^3$ is $1$ .

1. To find GCF:

The GCF of $12,8$ and $1$ is $1$ .

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

Compare $a$ and $a^2$ . Use $a$ .

Compare $r^2$ and $r^3$ . Use $r^2$ .

  $\text{GCF}=1\cdot a\cdot r^2=a{r}^2$

2. To find LCM:

The LCM of $12,8$ and $1$ is

  $2^3\cdot 3=24$

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

Compare $a$ and $a^2$ . Use $a^2$ .

Compare $r^2$ and $r^3$ . Use $r^3$ .

Compare $s^3$ and $s$ . Use $s^3$ .

  $\text{LCM}=24\cdot a^2\cdot r^3\cdot s^3=24a^2{r}^3{s}^3$

Therefore, for the given monomials, the GCF is $a{r}^2$ and LCM is $24a^2{r}^3{s}^3$ .