Solution: The LCM of 105 and 120 is 840
Methods
How to find the LCM of 105 and 120 using Prime Factorization
One way to find the LCM of 105 and 120 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 105?
What are the Factors of 120?
Here is the prime factorization of 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 1 × 7 1
And this is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 3 1 × 5 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: 3, 5, 7, 2
2
3
×
3
1
×
5
1
×
7
1
=
840
2^3 × 3^1 × 5^1 × 7^1 = 840
2 3 × 3 1 × 5 1 × 7 1 = 840
Through this we see that the LCM of 105 and 120 is 840.
How to Find the LCM of 105 and 120 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 105 and 120 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, 105 and 120:
What are the Multiples of 105?
What are the Multiples of 120?
Let’s take a look at the first 10 multiples for each of these numbers, 105 and 120:
First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050
First 10 Multiples of 120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200
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 105 and 120 are 840, 1680, 2520. Because 840 is the smallest, it is the least common multiple.
The LCM of 105 and 120 is 840.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 81 and 35?
What is the LCM of 140 and 87?
What is the LCM of 2 and 124?
What is the LCM of 134 and 112?
What is the LCM of 94 and 42?