Solution: The LCM of 65 and 109 is 7085
Methods
How to find the LCM of 65 and 109 using Prime Factorization
One way to find the LCM of 65 and 109 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 65?
What are the Factors of 109?
Here is the prime factorization of 65:
5
1
×
1
3
1
5^1 × 13^1
5 1 × 1 3 1
And this is the prime factorization of 109:
10
9
1
109^1
10 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: 5, 13, 109
5
1
×
1
3
1
×
10
9
1
=
7085
5^1 × 13^1 × 109^1 = 7085
5 1 × 1 3 1 × 10 9 1 = 7085
Through this we see that the LCM of 65 and 109 is 7085.
How to Find the LCM of 65 and 109 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 65 and 109 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, 65 and 109:
What are the Multiples of 65?
What are the Multiples of 109?
Let’s take a look at the first 10 multiples for each of these numbers, 65 and 109:
First 10 Multiples of 65: 65, 130, 195, 260, 325, 390, 455, 520, 585, 650
First 10 Multiples of 109: 109, 218, 327, 436, 545, 654, 763, 872, 981, 1090
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 65 and 109 are 7085, 14170, 21255. Because 7085 is the smallest, it is the least common multiple.
The LCM of 65 and 109 is 7085.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 4 and 2?
What is the LCM of 50 and 61?
What is the LCM of 145 and 117?
What is the LCM of 104 and 150?
What is the LCM of 100 and 82?