Solution: The LCM of 68 and 112 is 1904
Methods
How to find the LCM of 68 and 112 using Prime Factorization
One way to find the LCM of 68 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 68?
What are the Factors of 112?
Here is the prime factorization of 68:
2
2
×
1
7
1
2^2 × 17^1
2 2 × 1 7 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, 17, 7
2
4
×
7
1
×
1
7
1
=
1904
2^4 × 7^1 × 17^1 = 1904
2 4 × 7 1 × 1 7 1 = 1904
Through this we see that the LCM of 68 and 112 is 1904.
How to Find the LCM of 68 and 112 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 68 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, 68 and 112:
What are the Multiples of 68?
What are the Multiples of 112?
Let’s take a look at the first 10 multiples for each of these numbers, 68 and 112:
First 10 Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680
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 68 and 112 are 1904, 3808, 5712. Because 1904 is the smallest, it is the least common multiple.
The LCM of 68 and 112 is 1904.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 110 and 42?
What is the LCM of 41 and 37?
What is the LCM of 52 and 72?
What is the LCM of 90 and 145?
What is the LCM of 17 and 87?