Solution: The LCM of 139 and 68 is 9452
Methods
How to find the LCM of 139 and 68 using Prime Factorization
One way to find the LCM of 139 and 68 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 139?
What are the Factors of 68?
Here is the prime factorization of 139:
13
9
1
139^1
13 9 1
And this is the prime factorization of 68:
2
2
×
1
7
1
2^2 × 17^1
2 2 × 1 7 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: 139, 2, 17
2
2
×
1
7
1
×
13
9
1
=
9452
2^2 × 17^1 × 139^1 = 9452
2 2 × 1 7 1 × 13 9 1 = 9452
Through this we see that the LCM of 139 and 68 is 9452.
How to Find the LCM of 139 and 68 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 139 and 68 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, 139 and 68:
What are the Multiples of 139?
What are the Multiples of 68?
Let’s take a look at the first 10 multiples for each of these numbers, 139 and 68:
First 10 Multiples of 139: 139, 278, 417, 556, 695, 834, 973, 1112, 1251, 1390
First 10 Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680
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 139 and 68 are 9452, 18904, 28356. Because 9452 is the smallest, it is the least common multiple.
The LCM of 139 and 68 is 9452.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 4 and 106?
What is the LCM of 52 and 6?
What is the LCM of 88 and 54?
What is the LCM of 31 and 122?
What is the LCM of 108 and 61?