Chapter 4.4, Problem 22WE

(a).

To determine

To find: the GCF of the given monomials.

Answer to Problem 22WE

The GCF of $98a^2{b}^{2}c$ and $-{\text{70abc}}^2$ is $14abc$ .

Explanation of Solution

Given information:

The given monomials:

  $98a^2{b}^{2}c,-{\text{70abc}}^2$

Calculation:

The prime factorization of the coefficients are:

  $\begin{array}{l}98=2\cdot 7^2\\ 70=2\cdot 5\cdot 7\end{array}$

The GCF of $98$ and $-70$ is

  $2\cdot 7=14$

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

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

Compare $b^2$ and $b$ . Use $b$ .

Compare $c$ and $c^2$ . Use $c$ .

  $\text{GCF}=14\cdot a\cdot b\cdot c=14abc$

Therefore, the GCF of $98a^2{b}^{2}c$ and $-{\text{70abc}}^2$ is $14abc$ .

(b).

To determine

The LCM of the given monomials.

Answer to Problem 22WE

The LCM of $98a^2{b}^{2}c$ and $-{\text{70abc}}^2$ is $490a^2{b}^2{c}^2$ .

Explanation of Solution

Given information:

The given monomials:

  $98a^2{b}^{2}c,-{\text{70abc}}^2$

Calculation:

As per problem,

The prime factorization of the coefficients are:

  $\begin{array}{l}98=2\cdot 7^2\\ 70=2\cdot 5\cdot 7\end{array}$

The LCM of $98$ and $-70$ is

  $2\cdot 5\cdot 7^2=490$

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

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

Compare $b^2$ and $b$ . Use $b^2$ .

Compare $c$ and $c^2$ . Use $c^2$ .

  $\text{LCM}=490\cdot a^2\cdot b^2\cdot c^2=490a^2{b}^2{c}^2$

Therefore, the LCM of $98a^2{b}^{2}c$ and $-{\text{70abc}}^2$ is $490a^2{b}^2{c}^2$ .