Solution: The LCM of 146 and 77 is 11242
Methods
How to find the LCM of 146 and 77 using Prime Factorization
One way to find the LCM of 146 and 77 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 77?
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 77:
7
1
×
1
1
1
7^1 × 11^1
7 1 × 1 1 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, 7, 11
2
1
×
7
1
×
1
1
1
×
7
3
1
=
11242
2^1 × 7^1 × 11^1 × 73^1 = 11242
2 1 × 7 1 × 1 1 1 × 7 3 1 = 11242
Through this we see that the LCM of 146 and 77 is 11242.
How to Find the LCM of 146 and 77 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 146 and 77 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 77:
What are the Multiples of 146?
What are the Multiples of 77?
Let’s take a look at the first 10 multiples for each of these numbers, 146 and 77:
First 10 Multiples of 146: 146, 292, 438, 584, 730, 876, 1022, 1168, 1314, 1460
First 10 Multiples of 77: 77, 154, 231, 308, 385, 462, 539, 616, 693, 770
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 77 are 11242, 22484, 33726. Because 11242 is the smallest, it is the least common multiple.
The LCM of 146 and 77 is 11242.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 143 and 75?
What is the LCM of 67 and 37?
What is the LCM of 111 and 85?
What is the LCM of 139 and 46?
What is the LCM of 16 and 26?