Solution: The LCM of 130 and 112 is 7280
Methods
How to find the LCM of 130 and 112 using Prime Factorization
One way to find the LCM of 130 and 112 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 130?
What are the Factors of 112?
Here is the prime factorization of 130:
2
1
×
5
1
×
1
3
1
2^1 × 5^1 × 13^1
2 1 × 5 1 × 1 3 1
And this is the prime factorization of 112:
2
4
×
7
1
2^4 × 7^1
2 4 × 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: 2, 5, 13, 7
2
4
×
5
1
×
7
1
×
1
3
1
=
7280
2^4 × 5^1 × 7^1 × 13^1 = 7280
2 4 × 5 1 × 7 1 × 1 3 1 = 7280
Through this we see that the LCM of 130 and 112 is 7280.
How to Find the LCM of 130 and 112 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 130 and 112 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, 130 and 112:
What are the Multiples of 130?
What are the Multiples of 112?
Let’s take a look at the first 10 multiples for each of these numbers, 130 and 112:
First 10 Multiples of 130: 130, 260, 390, 520, 650, 780, 910, 1040, 1170, 1300
First 10 Multiples of 112: 112, 224, 336, 448, 560, 672, 784, 896, 1008, 1120
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 130 and 112 are 7280, 14560, 21840. Because 7280 is the smallest, it is the least common multiple.
The LCM of 130 and 112 is 7280.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 39 and 128?
What is the LCM of 113 and 12?
What is the LCM of 117 and 31?
What is the LCM of 10 and 109?
What is the LCM of 77 and 111?