Solution: The LCM of 69 and 146 is 10074
Methods
How to find the LCM of 69 and 146 using Prime Factorization
One way to find the LCM of 69 and 146 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 69?
What are the Factors of 146?
Here is the prime factorization of 69:
3
1
×
2
3
1
3^1 × 23^1
3 1 × 2 3 1
And this is the prime factorization of 146:
2
1
×
7
3
1
2^1 × 73^1
2 1 × 7 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: 3, 23, 2, 73
2
1
×
3
1
×
2
3
1
×
7
3
1
=
10074
2^1 × 3^1 × 23^1 × 73^1 = 10074
2 1 × 3 1 × 2 3 1 × 7 3 1 = 10074
Through this we see that the LCM of 69 and 146 is 10074.
How to Find the LCM of 69 and 146 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 69 and 146 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, 69 and 146:
What are the Multiples of 69?
What are the Multiples of 146?
Let’s take a look at the first 10 multiples for each of these numbers, 69 and 146:
First 10 Multiples of 69: 69, 138, 207, 276, 345, 414, 483, 552, 621, 690
First 10 Multiples of 146: 146, 292, 438, 584, 730, 876, 1022, 1168, 1314, 1460
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 69 and 146 are 10074, 20148, 30222. Because 10074 is the smallest, it is the least common multiple.
The LCM of 69 and 146 is 10074.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 87 and 43?
What is the LCM of 97 and 138?
What is the LCM of 65 and 46?
What is the LCM of 13 and 20?
What is the LCM of 108 and 141?