Solution: The LCM of 124 and 143 is 17732
Methods
How to find the LCM of 124 and 143 using Prime Factorization
One way to find the LCM of 124 and 143 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 124?
What are the Factors of 143?
Here is the prime factorization of 124:
2
2
×
3
1
1
2^2 × 31^1
2 2 × 3 1 1
And this is the prime factorization of 143:
1
1
1
×
1
3
1
11^1 × 13^1
1 1 1 × 1 3 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: 2, 31, 11, 13
2
2
×
1
1
1
×
1
3
1
×
3
1
1
=
17732
2^2 × 11^1 × 13^1 × 31^1 = 17732
2 2 × 1 1 1 × 1 3 1 × 3 1 1 = 17732
Through this we see that the LCM of 124 and 143 is 17732.
How to Find the LCM of 124 and 143 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 124 and 143 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, 124 and 143:
What are the Multiples of 124?
What are the Multiples of 143?
Let’s take a look at the first 10 multiples for each of these numbers, 124 and 143:
First 10 Multiples of 124: 124, 248, 372, 496, 620, 744, 868, 992, 1116, 1240
First 10 Multiples of 143: 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, 1430
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 124 and 143 are 17732, 35464, 53196. Because 17732 is the smallest, it is the least common multiple.
The LCM of 124 and 143 is 17732.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 110 and 127?
What is the LCM of 47 and 122?
What is the LCM of 43 and 42?
What is the LCM of 53 and 102?
What is the LCM of 31 and 115?