Chapter 4.4, Problem 23WE

(a).

To determine

To find: the GCF of the given monomials.

Answer to Problem 23WE

The GCF of $14ab,\text{ 14}bc$ and $\text{21}ac$ is $7$

Explanation of Solution

Given information:

The given monomials:

  $14ab,\text{ 14}bc\text{, 21}ac$

Calculation:

The prime factorization of the coefficients are:

The coefficient of first two monomials is same.

  $\begin{array}{l}14=2\cdot 7\\ 21=3\cdot 7\end{array}$

The GCF of $14$ and $21$ is $7$

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

As no one variable occurs in all three monomials,

  $\text{GCF}=7$

Therefore, the GCF of $14ab,\text{ 14}bc$ and $\text{21}ac$ is $7$

(b).

To determine

The LCM of the given monomials.

Answer to Problem 23WE

The LCM of $14ab,\text{ 14}bc$ and $\text{21}ac$ is $42abc$ .

Explanation of Solution

Given information:

The given monomials:

  $14ab,\text{ 14}bc\text{, 21}ac$

Calculation:

As per problem,

The prime factorization of the coefficients are:

The coefficient of first two monomials is same.

  $\begin{array}{l}14=2\cdot 7\\ 21=3\cdot 7\end{array}$

The LCM $14$ and $21$ is

  $2\cdot 3\cdot 7=42$

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

Use $a$ .

Use $b$ .

Use $c$ .

  $\text{LCM}=42\cdot a\cdot b\cdot c=42abc$

Therefore, the LCM of $14ab,\text{ 14}bc$ and $\text{21}ac$ is $42abc$ .