Solution: The LCM of 106 and 35 is 3710
Methods
How to find the LCM of 106 and 35 using Prime Factorization
One way to find the LCM of 106 and 35 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 106?
What are the Factors of 35?
Here is the prime factorization of 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 3 1
And this is the prime factorization of 35:
5
1
×
7
1
5^1 × 7^1
5 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: 2, 53, 5, 7
2
1
×
5
1
×
7
1
×
5
3
1
=
3710
2^1 × 5^1 × 7^1 × 53^1 = 3710
2 1 × 5 1 × 7 1 × 5 3 1 = 3710
Through this we see that the LCM of 106 and 35 is 3710.
How to Find the LCM of 106 and 35 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 106 and 35 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, 106 and 35:
What are the Multiples of 106?
What are the Multiples of 35?
Let’s take a look at the first 10 multiples for each of these numbers, 106 and 35:
First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060
First 10 Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350
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 106 and 35 are 3710, 7420, 11130. Because 3710 is the smallest, it is the least common multiple.
The LCM of 106 and 35 is 3710.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 129 and 119?
What is the LCM of 83 and 43?
What is the LCM of 54 and 39?
What is the LCM of 72 and 60?
What is the LCM of 78 and 53?