Solution: The LCM of 30 and 119 is 3570
Methods
How to find the LCM of 30 and 119 using Prime Factorization
One way to find the LCM of 30 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 30?
What are the Factors of 119?
Here is the prime factorization of 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 3 1 × 5 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: 2, 3, 5, 7, 17
2
1
×
3
1
×
5
1
×
7
1
×
1
7
1
=
3570
2^1 × 3^1 × 5^1 × 7^1 × 17^1 = 3570
2 1 × 3 1 × 5 1 × 7 1 × 1 7 1 = 3570
Through this we see that the LCM of 30 and 119 is 3570.
How to Find the LCM of 30 and 119 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 30 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, 30 and 119:
What are the Multiples of 30?
What are the Multiples of 119?
Let’s take a look at the first 10 multiples for each of these numbers, 30 and 119:
First 10 Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300
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 30 and 119 are 3570, 7140, 10710. Because 3570 is the smallest, it is the least common multiple.
The LCM of 30 and 119 is 3570.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 149 and 104?
What is the LCM of 12 and 81?
What is the LCM of 85 and 32?
What is the LCM of 74 and 35?
What is the LCM of 36 and 46?