Solution: The LCM of 103 and 114 is 11742
Methods
How to find the LCM of 103 and 114 using Prime Factorization
One way to find the LCM of 103 and 114 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 103?
What are the Factors of 114?
Here is the prime factorization of 103:
10
3
1
103^1
10 3 1
And this is the prime factorization of 114:
2
1
×
3
1
×
1
9
1
2^1 × 3^1 × 19^1
2 1 × 3 1 × 1 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: 103, 2, 3, 19
2
1
×
3
1
×
1
9
1
×
10
3
1
=
11742
2^1 × 3^1 × 19^1 × 103^1 = 11742
2 1 × 3 1 × 1 9 1 × 10 3 1 = 11742
Through this we see that the LCM of 103 and 114 is 11742.
How to Find the LCM of 103 and 114 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 103 and 114 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, 103 and 114:
What are the Multiples of 103?
What are the Multiples of 114?
Let’s take a look at the first 10 multiples for each of these numbers, 103 and 114:
First 10 Multiples of 103: 103, 206, 309, 412, 515, 618, 721, 824, 927, 1030
First 10 Multiples of 114: 114, 228, 342, 456, 570, 684, 798, 912, 1026, 1140
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 103 and 114 are 11742, 23484, 35226. Because 11742 is the smallest, it is the least common multiple.
The LCM of 103 and 114 is 11742.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 87 and 136?
What is the LCM of 18 and 74?
What is the LCM of 67 and 127?
What is the LCM of 19 and 10?
What is the LCM of 50 and 141?