Solution: The LCM of 145 and 149 is 21605
Methods
How to find the LCM of 145 and 149 using Prime Factorization
One way to find the LCM of 145 and 149 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 149?
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 149:
14
9
1
149^1
14 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: 5, 29, 149
5
1
×
2
9
1
×
14
9
1
=
21605
5^1 × 29^1 × 149^1 = 21605
5 1 × 2 9 1 × 14 9 1 = 21605
Through this we see that the LCM of 145 and 149 is 21605.
How to Find the LCM of 145 and 149 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 145 and 149 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 149:
What are the Multiples of 145?
What are the Multiples of 149?
Let’s take a look at the first 10 multiples for each of these numbers, 145 and 149:
First 10 Multiples of 145: 145, 290, 435, 580, 725, 870, 1015, 1160, 1305, 1450
First 10 Multiples of 149: 149, 298, 447, 596, 745, 894, 1043, 1192, 1341, 1490
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 149 are 21605, 43210, 64815. Because 21605 is the smallest, it is the least common multiple.
The LCM of 145 and 149 is 21605.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 105 and 119?
What is the LCM of 22 and 127?
What is the LCM of 120 and 78?
What is the LCM of 14 and 17?
What is the LCM of 89 and 113?