Solution: The LCM of 110 and 26 is 1430
Methods
How to find the LCM of 110 and 26 using Prime Factorization
One way to find the LCM of 110 and 26 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 110?
What are the Factors of 26?
Here is the prime factorization of 110:
2
1
×
5
1
×
1
1
1
2^1 × 5^1 × 11^1
2 1 × 5 1 × 1 1 1
And this is the prime factorization of 26:
2
1
×
1
3
1
2^1 × 13^1
2 1 × 1 3 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, 5, 11, 13
2
1
×
5
1
×
1
1
1
×
1
3
1
=
1430
2^1 × 5^1 × 11^1 × 13^1 = 1430
2 1 × 5 1 × 1 1 1 × 1 3 1 = 1430
Through this we see that the LCM of 110 and 26 is 1430.
How to Find the LCM of 110 and 26 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 110 and 26 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, 110 and 26:
What are the Multiples of 110?
What are the Multiples of 26?
Let’s take a look at the first 10 multiples for each of these numbers, 110 and 26:
First 10 Multiples of 110: 110, 220, 330, 440, 550, 660, 770, 880, 990, 1100
First 10 Multiples of 26: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260
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 110 and 26 are 1430, 2860, 4290. Because 1430 is the smallest, it is the least common multiple.
The LCM of 110 and 26 is 1430.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 41 and 133?
What is the LCM of 127 and 80?
What is the LCM of 22 and 100?
What is the LCM of 11 and 87?
What is the LCM of 135 and 143?