Solution: The LCM of 26 and 29 is 754
Methods
How to find the LCM of 26 and 29 using Prime Factorization
One way to find the LCM of 26 and 29 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 26?
What are the Factors of 29?
Here is the prime factorization of 26:
2
1
×
1
3
1
2^1 × 13^1
2 1 × 1 3 1
And this is the prime factorization of 29:
2
9
1
29^1
2 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: 2, 13, 29
2
1
×
1
3
1
×
2
9
1
=
754
2^1 × 13^1 × 29^1 = 754
2 1 × 1 3 1 × 2 9 1 = 754
Through this we see that the LCM of 26 and 29 is 754.
How to Find the LCM of 26 and 29 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 26 and 29 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, 26 and 29:
What are the Multiples of 26?
What are the Multiples of 29?
Let’s take a look at the first 10 multiples for each of these numbers, 26 and 29:
First 10 Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260
First 10 Multiples of 29: 29, 58, 87, 116, 145, 174, 203, 232, 261, 290
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 26 and 29 are 754, 1508, 2262. Because 754 is the smallest, it is the least common multiple.
The LCM of 26 and 29 is 754.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 150 and 125?
What is the LCM of 70 and 58?
What is the LCM of 23 and 117?
What is the LCM of 133 and 110?
What is the LCM of 6 and 48?