Solution: The LCM of 122 and 145 is 17690
Methods
How to find the LCM of 122 and 145 using Prime Factorization
One way to find the LCM of 122 and 145 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 145?
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 145:
5
1
×
2
9
1
5^1 × 29^1
5 1 × 2 9 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, 5, 29
2
1
×
5
1
×
2
9
1
×
6
1
1
=
17690
2^1 × 5^1 × 29^1 × 61^1 = 17690
2 1 × 5 1 × 2 9 1 × 6 1 1 = 17690
Through this we see that the LCM of 122 and 145 is 17690.
How to Find the LCM of 122 and 145 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 122 and 145 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 145:
What are the Multiples of 122?
What are the Multiples of 145?
Let’s take a look at the first 10 multiples for each of these numbers, 122 and 145:
First 10 Multiples of 122: 122, 244, 366, 488, 610, 732, 854, 976, 1098, 1220
First 10 Multiples of 145: 145, 290, 435, 580, 725, 870, 1015, 1160, 1305, 1450
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 145 are 17690, 35380, 53070. Because 17690 is the smallest, it is the least common multiple.
The LCM of 122 and 145 is 17690.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 81 and 60?
What is the LCM of 5 and 98?
What is the LCM of 97 and 63?
What is the LCM of 80 and 18?
What is the LCM of 128 and 119?