Solution: The LCM of 67 and 146 is 9782
Methods
How to find the LCM of 67 and 146 using Prime Factorization
One way to find the LCM of 67 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 67?
What are the Factors of 146?
Here is the prime factorization of 67:
6
7
1
67^1
6 7 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: 67, 2, 73
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 67 and 146 is 9782.
How to Find the LCM of 67 and 146 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 67 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, 67 and 146:
What are the Multiples of 67?
What are the Multiples of 146?
Let’s take a look at the first 10 multiples for each of these numbers, 67 and 146:
First 10 Multiples of 67: 67, 134, 201, 268, 335, 402, 469, 536, 603, 670
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 67 and 146 are 9782, 19564, 29346. Because 9782 is the smallest, it is the least common multiple.
The LCM of 67 and 146 is 9782.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 56 and 55?
What is the LCM of 129 and 99?
What is the LCM of 123 and 9?
What is the LCM of 79 and 35?
What is the LCM of 46 and 115?