Solution: The LCM of 10 and 127 is 1270
Methods
How to find the LCM of 10 and 127 using Prime Factorization
One way to find the LCM of 10 and 127 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 10?
What are the Factors of 127?
Here is the prime factorization of 10:
2
1
×
5
1
2^1 × 5^1
2 1 × 5 1
And this is the prime factorization of 127:
12
7
1
127^1
12 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, 5, 127
2
1
×
5
1
×
12
7
1
=
1270
2^1 × 5^1 × 127^1 = 1270
2 1 × 5 1 × 12 7 1 = 1270
Through this we see that the LCM of 10 and 127 is 1270.
How to Find the LCM of 10 and 127 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 10 and 127 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, 10 and 127:
What are the Multiples of 10?
What are the Multiples of 127?
Let’s take a look at the first 10 multiples for each of these numbers, 10 and 127:
First 10 Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
First 10 Multiples of 127: 127, 254, 381, 508, 635, 762, 889, 1016, 1143, 1270
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 10 and 127 are 1270, 2540, 3810. Because 1270 is the smallest, it is the least common multiple.
The LCM of 10 and 127 is 1270.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 105 and 47?
What is the LCM of 85 and 82?
What is the LCM of 39 and 88?
What is the LCM of 33 and 70?
What is the LCM of 124 and 83?