Solution: The LCM of 39 and 19 is 741
Methods
How to find the LCM of 39 and 19 using Prime Factorization
One way to find the LCM of 39 and 19 is to start by comparing the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 39?
What are the Factors of 19?
Here is the prime factorization of 39:
3
1
×
1
3
1
3^1 × 13^1
3 1 × 1 3 1
And this is the prime factorization of 19:
1
9
1
19^1
1 9 1
When you compare the prime factorization of these two numbers, you want to look for the highest power that each prime factor is raised to. In this case, there are these prime factors to consider: 3, 13, 19
3
1
×
1
3
1
×
1
9
1
=
741
3^1 × 13^1 × 19^1 = 741
3 1 × 1 3 1 × 1 9 1 = 741
Through this we see that the LCM of 39 and 19 is 741.
How to Find the LCM of 39 and 19 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 39 and 19 is to begin to list a few multiples for each number. If you need a refresher on how to find the multiples of these numbers, you can see the walkthroughs in the links below for each number.
Let’s take a look at the multiples for each of these numbers, 39 and 19:
What are the Multiples of 39?
What are the Multiples of 19?
Let’s take a look at the first 10 multiples for each of these numbers, 39 and 19:
First 10 Multiples of 39: 39, 78, 117, 156, 195, 234, 273, 312, 351, 390
First 10 Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, 190
You can continue to list out the multiples of these numbers as long as needed to find a match. Once you do find a match, or several matches, the smallest of these matches would be the Least Common Multiple. For instance, the first matching multiple(s) of 39 and 19 are 741, 1482, 2223. Because 741 is the smallest, it is the least common multiple.
The LCM of 39 and 19 is 741.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 6 and 137?
What is the LCM of 91 and 23?
What is the LCM of 70 and 64?
What is the LCM of 15 and 12?
What is the LCM of 25 and 1?