Solution: The LCM of 145 and 37 is 5365
Methods
How to find the LCM of 145 and 37 using Prime Factorization
One way to find the LCM of 145 and 37 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 37?
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 37:
3
7
1
37^1
3 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: 5, 29, 37
5
1
×
2
9
1
×
3
7
1
=
5365
5^1 × 29^1 × 37^1 = 5365
5 1 × 2 9 1 × 3 7 1 = 5365
Through this we see that the LCM of 145 and 37 is 5365.
How to Find the LCM of 145 and 37 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 145 and 37 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 37:
What are the Multiples of 145?
What are the Multiples of 37?
Let’s take a look at the first 10 multiples for each of these numbers, 145 and 37:
First 10 Multiples of 145: 145, 290, 435, 580, 725, 870, 1015, 1160, 1305, 1450
First 10 Multiples of 37: 37, 74, 111, 148, 185, 222, 259, 296, 333, 370
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 37 are 5365, 10730, 16095. Because 5365 is the smallest, it is the least common multiple.
The LCM of 145 and 37 is 5365.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 48 and 90?
What is the LCM of 129 and 85?
What is the LCM of 6 and 138?
What is the LCM of 56 and 97?
What is the LCM of 96 and 141?