Chapter 1.3, Problem 71CCR

To determine

The least common multiple (LCM) of 9 and 12.

Answer to Problem 71CCR

  $36$

Explanation of Solution

Given:

The pair of numbers, 9 and 12.

Concept Used:

LCM(least common multiple) of a list of numbers can be found using following steps,

1. Write prime factorization of each number
2. Find the product ofcommon factors that appear in each number and the remaining prime factors from each number that are not common.

Calculation:

In order to find the least common multiple of the given number, first find the prime factorization of each number as shown below,

  $\begin{array}{l}9=3\times 3\\ 12=2\times 2\times 3\end{array}$

Here observe that the factor 3 is common andoccur once in each number. Apart from this the remaining factor from both numbers are 3, 2 and 2. So, the least common multiple of the numbers would be the product of common factor and the remaining factors as shown below:

  $\begin{array}{l}\text{LCM of 9 and 12 is:}\\ 3\times 3\times 2\times 2=36\end{array}$

Thus, the least common multiple (LCM) of the given numbers is $36$ .