Chapter 4.4, Problem 9WE

(a).

To determine

To find: the GCF of the given monomials.

Answer to Problem 9WE

The GCF of $20$ and $35$ is $5$

Explanation of Solution

Given information :

The given monomials:

  $\text{20,3}5$

Calculation :

As per problem,

The prime factorization of the given monomials are:

  $\begin{array}{l}20=2^2\cdot 5\text{}\text{}\text{}\\ 35=5\cdot 7\end{array}$

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

  $\text{GCF}=5$

Therefore, the GCF of $20$ and $35$ is $5$

(b).

To determine

The LCM of the given monomials.

Answer to Problem 9WE

The LCM of $20$ and $35$ is $140$

Explanation of Solution

Given information :

The given monomials:

  $\text{20, }35$

Calculation :

As per problem,

The prime factorization of the given monomials are:

  $\begin{array}{l}20=2^2\cdot 5\text{}\text{}\text{}\\ 35=5\cdot 7\end{array}$

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

  $\text{LCM}=2^2\cdot 5\cdot 7=140$

Therefore, the LCM of $20$ and $35$ is $140$