Chapter 4.4, Problem 12WE

(a).

To determine

To find: the GCF of the given monomials.

Answer to Problem 12WE

The GCF of $315$ and $-525$ is $105$

Explanation of Solution

Given information :

The given monomials:

  $\text{315,}-525$

Calculation :

As per problem,

The prime factorization of the given monomials are:

  $\begin{array}{l}315=3^2\cdot 5\cdot 7\\ 525=3\cdot 5^2\cdot 7\end{array}$

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

  $\text{GCF}=3\cdot 5\cdot 7=105$

Therefore, the GCF of $315$ and $-525$ is $105$

(b).

To determine

The LCM of the given monomials.

Answer to Problem 12WE

The LCM of $315$ and $-525$ is $1575$

Explanation of Solution

Given information :

The given monomials:

  $\text{315,}-525$

Calculation :

As per problem,

The prime factorization of the given monomials are:

  $\begin{array}{l}315=3^2\cdot 5\cdot 7\\ 525=3\cdot 5^2\cdot 7\end{array}$

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

  $\text{LCM}=3^2\cdot 5^2\cdot 7=1575$

Therefore, the LCM of $315$ and $-525$ is $1575$