Chapter 11.5, Problem 78S

To determine

To calculate: To find the least common multiple for the set of numbers

Answer to Problem 78S

The least common multiple of given set of number is $60$

Explanation of Solution

Given information: Set of numbers are $5,12,15$

Formula Used:

Least Common Multiple of two numbers is the smallest number that is the multiple of both the numbers

In order to find the least common multiple of numbers, first list the prime factors of all numbers and then multiply each factor the greatest number of time it occurs in either numbers.

Calculation:

Set of numbers are given as follows:

  $5,12,15$

Prime factors of $5=5$

Prime factors of $12=2\times 2\times 3$

Prime factors of $15=5\times 3$

Thus. Least Common Multiple is calculated as follows:

  $\begin{array}{l}LCM=2\times 2\times 5\times 3\\ LCM=60\end{array}$

Conclusion:

Hence, least common multiple of given set of number is $60$