Chapter 4.4, Problem 11WE

(a).

To determine

To find: the GCF of the given monomials.

Answer to Problem 11WE

The GCF of $-48$ and $108$ is $12$

Explanation of Solution

Given information :

The given monomials:

  $-\text{48, }108$

Calculation :

As per problem,

The prime factorization of the given monomials are:

  $\begin{array}{l}48=2^4\cdot 3\\ 108=2^2\cdot 3^3\end{array}$

To find GCF, take the least power of each common prime factor.

  $\text{GCF}=2^2\cdot 3=12$

Therefore, the GCF of $-48$ and $108$ is $12$

(b).

To determine

The LCM of the given monomials.

Answer to Problem 11WE

The LCM of $-48$ and $108$ is $432$

Explanation of Solution

Given information :

The given monomials:

  $-\text{48, }108$

Calculation :

As per problem,

The prime factorization of the given monomials are:

  $\begin{array}{l}48=2^4\cdot 3\\ 108=2^2\cdot 3^3\end{array}$

To find LCM, take the greatest power of each prime factor.

  $\text{LCM}=2^4\cdot 3^3=432$

Therefore, the LCM of $-48$ and $108$ is $432$