Solution: The LCM of 145 and 121 is 17545
Methods
How to find the LCM of 145 and 121 using Prime Factorization
One way to find the LCM of 145 and 121 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 145?
What are the Factors of 121?
Here is the prime factorization of 145:
5
1
×
2
9
1
5^1 × 29^1
5 1 × 2 9 1
And this is the prime factorization of 121:
1
1
2
11^2
1 1 2
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: 5, 29, 11
5
1
×
1
1
2
×
2
9
1
=
17545
5^1 × 11^2 × 29^1 = 17545
5 1 × 1 1 2 × 2 9 1 = 17545
Through this we see that the LCM of 145 and 121 is 17545.
How to Find the LCM of 145 and 121 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 145 and 121 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, 145 and 121:
What are the Multiples of 145?
What are the Multiples of 121?
Let’s take a look at the first 10 multiples for each of these numbers, 145 and 121:
First 10 Multiples of 145: 145, 290, 435, 580, 725, 870, 1015, 1160, 1305, 1450
First 10 Multiples of 121: 121, 242, 363, 484, 605, 726, 847, 968, 1089, 1210
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 145 and 121 are 17545, 35090, 52635. Because 17545 is the smallest, it is the least common multiple.
The LCM of 145 and 121 is 17545.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 123 and 122?
What is the LCM of 54 and 58?
What is the LCM of 137 and 138?
What is the LCM of 20 and 72?
What is the LCM of 45 and 42?