Chapter 4.4, Problem 13OE

To determine

To find : the GCF and LCM of the given pair of integers.

Answer to Problem 13OE

For the given pair of integers, the GCF is $4$ and LCM is $24$

Explanation of Solution

Given information :

The given pair of integers:

  $8\text{ and }12$

Calculation :

As per problem,

The prime factorization of the given pair of integers are:

  $\begin{array}{l}8=2^3\text{}\text{}\text{}\\ 12=2^2\cdot 3\end{array}$

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

$\text{GCF}=2^2=4$

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

  $\text{LCM}=2^3\cdot 3=24$

Therefore, for the given pair of integers, the GCF is $4$ and LCM is $24$