Solution: The LCM of 149 and 119 is 17731
Methods
How to find the LCM of 149 and 119 using Prime Factorization
One way to find the LCM of 149 and 119 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 149?
What are the Factors of 119?
Here is the prime factorization of 149:
14
9
1
149^1
14 9 1
And this is the prime factorization of 119:
7
1
×
1
7
1
7^1 × 17^1
7 1 × 1 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: 149, 7, 17
7
1
×
1
7
1
×
14
9
1
=
17731
7^1 × 17^1 × 149^1 = 17731
7 1 × 1 7 1 × 14 9 1 = 17731
Through this we see that the LCM of 149 and 119 is 17731.
How to Find the LCM of 149 and 119 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 149 and 119 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, 149 and 119:
What are the Multiples of 149?
What are the Multiples of 119?
Let’s take a look at the first 10 multiples for each of these numbers, 149 and 119:
First 10 Multiples of 149: 149, 298, 447, 596, 745, 894, 1043, 1192, 1341, 1490
First 10 Multiples of 119: 119, 238, 357, 476, 595, 714, 833, 952, 1071, 1190
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 149 and 119 are 17731, 35462, 53193. Because 17731 is the smallest, it is the least common multiple.
The LCM of 149 and 119 is 17731.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 24 and 52?
What is the LCM of 80 and 58?
What is the LCM of 145 and 67?
What is the LCM of 25 and 31?
What is the LCM of 50 and 92?