Solution: The LCM of 22 and 77 is 154
Methods
How to find the LCM of 22 and 77 using Prime Factorization
One way to find the LCM of 22 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 22?
What are the Factors of 77?
Here is the prime factorization of 22:
2
1
×
1
1
1
2^1 × 11^1
2 1 × 1 1 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, 11, 7
2
1
×
7
1
×
1
1
1
=
154
2^1 × 7^1 × 11^1 = 154
2 1 × 7 1 × 1 1 1 = 154
Through this we see that the LCM of 22 and 77 is 154.
How to Find the LCM of 22 and 77 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 22 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, 22 and 77:
What are the Multiples of 22?
What are the Multiples of 77?
Let’s take a look at the first 10 multiples for each of these numbers, 22 and 77:
First 10 Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, 220
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 22 and 77 are 154, 308, 462. Because 154 is the smallest, it is the least common multiple.
The LCM of 22 and 77 is 154.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 86 and 6?
What is the LCM of 67 and 66?
What is the LCM of 134 and 18?
What is the LCM of 11 and 90?
What is the LCM of 102 and 25?