Solution: The LCM of 105 and 111 is 3885
Methods
How to find the LCM of 105 and 111 using Prime Factorization
One way to find the LCM of 105 and 111 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 111?
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 111:
3
1
×
3
7
1
3^1 × 37^1
3 1 × 3 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: 3, 5, 7, 37
3
1
×
5
1
×
7
1
×
3
7
1
=
3885
3^1 × 5^1 × 7^1 × 37^1 = 3885
3 1 × 5 1 × 7 1 × 3 7 1 = 3885
Through this we see that the LCM of 105 and 111 is 3885.
How to Find the LCM of 105 and 111 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 105 and 111 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 111:
What are the Multiples of 105?
What are the Multiples of 111?
Let’s take a look at the first 10 multiples for each of these numbers, 105 and 111:
First 10 Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050
First 10 Multiples of 111: 111, 222, 333, 444, 555, 666, 777, 888, 999, 1110
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 111 are 3885, 7770, 11655. Because 3885 is the smallest, it is the least common multiple.
The LCM of 105 and 111 is 3885.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 103 and 110?
What is the LCM of 23 and 20?
What is the LCM of 145 and 69?
What is the LCM of 127 and 14?
What is the LCM of 62 and 148?