Solution: The LCM of 109 and 139 is 15151
Methods
How to find the LCM of 109 and 139 using Prime Factorization
One way to find the LCM of 109 and 139 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 109?
What are the Factors of 139?
Here is the prime factorization of 109:
10
9
1
109^1
10 9 1
And this is the prime factorization of 139:
13
9
1
139^1
13 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: 109, 139
10
9
1
×
13
9
1
=
15151
109^1 × 139^1 = 15151
10 9 1 × 13 9 1 = 15151
Through this we see that the LCM of 109 and 139 is 15151.
How to Find the LCM of 109 and 139 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 109 and 139 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, 109 and 139:
What are the Multiples of 109?
What are the Multiples of 139?
Let’s take a look at the first 10 multiples for each of these numbers, 109 and 139:
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
First 10 Multiples of 139: 139, 278, 417, 556, 695, 834, 973, 1112, 1251, 1390
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 109 and 139 are 15151, 30302, 45453. Because 15151 is the smallest, it is the least common multiple.
The LCM of 109 and 139 is 15151.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 54 and 53?
What is the LCM of 142 and 33?
What is the LCM of 125 and 65?
What is the LCM of 55 and 140?
What is the LCM of 91 and 102?