Solution: The LCM of 68 and 29 is 1972
Methods
How to find the LCM of 68 and 29 using Prime Factorization
One way to find the LCM of 68 and 29 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 29?
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 29:
2
9
1
29^1
2 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: 2, 17, 29
2
2
×
1
7
1
×
2
9
1
=
1972
2^2 × 17^1 × 29^1 = 1972
2 2 × 1 7 1 × 2 9 1 = 1972
Through this we see that the LCM of 68 and 29 is 1972.
How to Find the LCM of 68 and 29 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 68 and 29 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 29:
What are the Multiples of 68?
What are the Multiples of 29?
Let’s take a look at the first 10 multiples for each of these numbers, 68 and 29:
First 10 Multiples of 68: 68, 136, 204, 272, 340, 408, 476, 544, 612, 680
First 10 Multiples of 29: 29, 58, 87, 116, 145, 174, 203, 232, 261, 290
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 29 are 1972, 3944, 5916. Because 1972 is the smallest, it is the least common multiple.
The LCM of 68 and 29 is 1972.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 64 and 136?
What is the LCM of 21 and 60?
What is the LCM of 145 and 67?
What is the LCM of 91 and 77?
What is the LCM of 130 and 54?