Solution: The LCM of 103 and 142 is 14626
Methods
How to find the LCM of 103 and 142 using Prime Factorization
One way to find the LCM of 103 and 142 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 142?
Here is the prime factorization of 103:
10
3
1
103^1
10 3 1
And this is the prime factorization of 142:
2
1
×
7
1
1
2^1 × 71^1
2 1 × 7 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: 103, 2, 71
2
1
×
7
1
1
×
10
3
1
=
14626
2^1 × 71^1 × 103^1 = 14626
2 1 × 7 1 1 × 10 3 1 = 14626
Through this we see that the LCM of 103 and 142 is 14626.
How to Find the LCM of 103 and 142 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 103 and 142 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 142:
What are the Multiples of 103?
What are the Multiples of 142?
Let’s take a look at the first 10 multiples for each of these numbers, 103 and 142:
First 10 Multiples of 103: 103, 206, 309, 412, 515, 618, 721, 824, 927, 1030
First 10 Multiples of 142: 142, 284, 426, 568, 710, 852, 994, 1136, 1278, 1420
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 142 are 14626, 29252, 43878. Because 14626 is the smallest, it is the least common multiple.
The LCM of 103 and 142 is 14626.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 42 and 38?
What is the LCM of 52 and 14?
What is the LCM of 5 and 29?
What is the LCM of 37 and 122?
What is the LCM of 17 and 101?