Solution: The LCM of 145 and 10 is 290
Methods
How to find the LCM of 145 and 10 using Prime Factorization
One way to find the LCM of 145 and 10 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 10?
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 10:
2
1
×
5
1
2^1 × 5^1
2 1 × 5 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, 2
2
1
×
5
1
×
2
9
1
=
290
2^1 × 5^1 × 29^1 = 290
2 1 × 5 1 × 2 9 1 = 290
Through this we see that the LCM of 145 and 10 is 290.
How to Find the LCM of 145 and 10 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 145 and 10 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 10:
What are the Multiples of 145?
What are the Multiples of 10?
Let’s take a look at the first 10 multiples for each of these numbers, 145 and 10:
First 10 Multiples of 145: 145, 290, 435, 580, 725, 870, 1015, 1160, 1305, 1450
First 10 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
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 10 are 290, 580, 870. Because 290 is the smallest, it is the least common multiple.
The LCM of 145 and 10 is 290.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 114 and 112?
What is the LCM of 126 and 106?
What is the LCM of 97 and 15?
What is the LCM of 136 and 131?
What is the LCM of 58 and 31?