Chapter SR4, Problem 45P

Solution

The least common multiple (LCM) of the numbers $27,81,\text{and 33}$ .

  $891$

Given:

The numbers $27,81,\text{and 33}$ .

Concept Used:

The LCM (Least Common Multiple) of a list of integers is the least integer that is divisible by all the integers in the list.

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 of common 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 numbers $27,81,\text{and 33}$ , find the prime factorization of each number and then multiply the factors that are common in each number and the remaining prime factors from each number that are not common to get the LCM of the numbers as shown below,

  $\begin{array}{l}\text{Prime factors of }27,81,\text{and 33:}\\ 27=3\times 3\times 3\\ 81=3\times 3\times 3\times 3\\ 33=3\times 11\\ \\ \text{LCM of }27,81,\text{and 33 is:}\\ 3\times 3\times 3\times 3\times 11=891\end{array}$

Thus, the least common multiple (LCM) of the given numbers is $891$ .