Solution: The LCM of 111 and 101 is 11211
Methods
How to find the LCM of 111 and 101 using Prime Factorization
One way to find the LCM of 111 and 101 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 111?
What are the Factors of 101?
Here is the prime factorization of 111:
3
1
×
3
7
1
3^1 × 37^1
3 1 × 3 7 1
And this is the prime factorization of 101:
10
1
1
101^1
10 1 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, 37, 101
3
1
×
3
7
1
×
10
1
1
=
11211
3^1 × 37^1 × 101^1 = 11211
3 1 × 3 7 1 × 10 1 1 = 11211
Through this we see that the LCM of 111 and 101 is 11211.
How to Find the LCM of 111 and 101 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 111 and 101 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, 111 and 101:
What are the Multiples of 111?
What are the Multiples of 101?
Let’s take a look at the first 10 multiples for each of these numbers, 111 and 101:
First 10 Multiples of 111: 111, 222, 333, 444, 555, 666, 777, 888, 999, 1110
First 10 Multiples of 101: 101, 202, 303, 404, 505, 606, 707, 808, 909, 1010
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 111 and 101 are 11211, 22422, 33633. Because 11211 is the smallest, it is the least common multiple.
The LCM of 111 and 101 is 11211.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 116 and 24?
What is the LCM of 45 and 50?
What is the LCM of 73 and 52?
What is the LCM of 133 and 118?
What is the LCM of 47 and 90?