Solution: The LCM of 146 and 134 is 9782
Methods
How to find the LCM of 146 and 134 using Prime Factorization
One way to find the LCM of 146 and 134 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 146?
What are the Factors of 134?
Here is the prime factorization of 146:
2
1
×
7
3
1
2^1 × 73^1
2 1 × 7 3 1
And this is the prime factorization of 134:
2
1
×
6
7
1
2^1 × 67^1
2 1 × 6 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, 73, 67
2
1
×
6
7
1
×
7
3
1
=
9782
2^1 × 67^1 × 73^1 = 9782
2 1 × 6 7 1 × 7 3 1 = 9782
Through this we see that the LCM of 146 and 134 is 9782.
How to Find the LCM of 146 and 134 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 146 and 134 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, 146 and 134:
What are the Multiples of 146?
What are the Multiples of 134?
Let’s take a look at the first 10 multiples for each of these numbers, 146 and 134:
First 10 Multiples of 146: 146, 292, 438, 584, 730, 876, 1022, 1168, 1314, 1460
First 10 Multiples of 134: 134, 268, 402, 536, 670, 804, 938, 1072, 1206, 1340
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 146 and 134 are 9782, 19564, 29346. Because 9782 is the smallest, it is the least common multiple.
The LCM of 146 and 134 is 9782.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 98 and 38?
What is the LCM of 139 and 34?
What is the LCM of 137 and 79?
What is the LCM of 120 and 35?
What is the LCM of 80 and 75?