Solution: The LCM of 122 and 126 is 7686
Methods
How to find the LCM of 122 and 126 using Prime Factorization
One way to find the LCM of 122 and 126 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 122?
What are the Factors of 126?
Here is the prime factorization of 122:
2
1
×
6
1
1
2^1 × 61^1
2 1 × 6 1 1
And this is the prime factorization of 126:
2
1
×
3
2
×
7
1
2^1 × 3^2 × 7^1
2 1 × 3 2 × 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, 61, 3, 7
2
1
×
3
2
×
7
1
×
6
1
1
=
7686
2^1 × 3^2 × 7^1 × 61^1 = 7686
2 1 × 3 2 × 7 1 × 6 1 1 = 7686
Through this we see that the LCM of 122 and 126 is 7686.
How to Find the LCM of 122 and 126 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 122 and 126 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, 122 and 126:
What are the Multiples of 122?
What are the Multiples of 126?
Let’s take a look at the first 10 multiples for each of these numbers, 122 and 126:
First 10 Multiples of 122: 122, 244, 366, 488, 610, 732, 854, 976, 1098, 1220
First 10 Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260
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 122 and 126 are 7686, 15372, 23058. Because 7686 is the smallest, it is the least common multiple.
The LCM of 122 and 126 is 7686.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 14 and 63?
What is the LCM of 65 and 138?
What is the LCM of 102 and 58?
What is the LCM of 81 and 148?
What is the LCM of 67 and 144?