Solution: The LCM of 17 and 122 is 2074
Methods
How to find the LCM of 17 and 122 using Prime Factorization
One way to find the LCM of 17 and 122 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 17?
What are the Factors of 122?
Here is the prime factorization of 17:
1
7
1
17^1
1 7 1
And this is the prime factorization of 122:
2
1
×
6
1
1
2^1 × 61^1
2 1 × 6 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: 17, 2, 61
2
1
×
1
7
1
×
6
1
1
=
2074
2^1 × 17^1 × 61^1 = 2074
2 1 × 1 7 1 × 6 1 1 = 2074
Through this we see that the LCM of 17 and 122 is 2074.
How to Find the LCM of 17 and 122 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 17 and 122 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, 17 and 122:
What are the Multiples of 17?
What are the Multiples of 122?
Let’s take a look at the first 10 multiples for each of these numbers, 17 and 122:
First 10 Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, 170
First 10 Multiples of 122: 122, 244, 366, 488, 610, 732, 854, 976, 1098, 1220
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 17 and 122 are 2074, 4148, 6222. Because 2074 is the smallest, it is the least common multiple.
The LCM of 17 and 122 is 2074.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 78 and 110?
What is the LCM of 69 and 50?
What is the LCM of 87 and 127?
What is the LCM of 58 and 90?
What is the LCM of 25 and 68?