Chapter 4.4, Problem 10WE

(a).

To determine

To find: the GCF of the given monomials.

Answer to Problem 10WE

The GCF of $\text{45}$ and $75$ is $15$

Explanation of Solution

Given information :

The given monomials:

  $\text{45, 7}5$

Calculation :

As per problem,

The prime factorization of the given monomials are:

  $\begin{array}{l}45=3^2\cdot 5\text{}\text{}\text{}\\ 75=3\cdot 5^2\end{array}$

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

  $\text{GCF}=3\cdot 5=15$

Therefore, the GCF of $\text{45}$ and $75$ is $15$

(b).

To determine

The LCM of the given monomials.

Answer to Problem 10WE

The LCMof $\text{45}$ and $75$ is $225$

Explanation of Solution

Given information :

The given monomials:

  $\text{45, 7}5$

Calculation :

As per problem,

The prime factorization of the given monomials are:

  $\begin{array}{l}45=3^2\cdot 5\text{}\text{}\text{}\\ 75=3\cdot 5^2\end{array}$

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

  $\text{LCM}=3^2\cdot 5^2=225$

Therefore, the LCM of $\text{45}$ and $75$ is $225$