Solution: The LCM of 14 and 75 is 1050
Methods
How to find the LCM of 14 and 75 using Prime Factorization
One way to find the LCM of 14 and 75 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 14?
What are the Factors of 75?
Here is the prime factorization of 14:
2
1
×
7
1
2^1 × 7^1
2 1 × 7 1
And this is the prime factorization of 75:
3
1
×
5
2
3^1 × 5^2
3 1 × 5 2
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, 7, 3, 5
2
1
×
3
1
×
5
2
×
7
1
=
1050
2^1 × 3^1 × 5^2 × 7^1 = 1050
2 1 × 3 1 × 5 2 × 7 1 = 1050
Through this we see that the LCM of 14 and 75 is 1050.
How to Find the LCM of 14 and 75 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 14 and 75 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, 14 and 75:
What are the Multiples of 14?
What are the Multiples of 75?
Let’s take a look at the first 10 multiples for each of these numbers, 14 and 75:
First 10 Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140
First 10 Multiples of 75: 75, 150, 225, 300, 375, 450, 525, 600, 675, 750
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 14 and 75 are 1050, 2100, 3150. Because 1050 is the smallest, it is the least common multiple.
The LCM of 14 and 75 is 1050.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 76 and 102?
What is the LCM of 94 and 37?
What is the LCM of 48 and 69?
What is the LCM of 67 and 15?
What is the LCM of 103 and 33?