Solution: The LCM of 127 and 135 is 17145
Methods
How to find the LCM of 127 and 135 using Prime Factorization
One way to find the LCM of 127 and 135 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 127?
What are the Factors of 135?
Here is the prime factorization of 127:
12
7
1
127^1
12 7 1
And this is the prime factorization of 135:
3
3
×
5
1
3^3 × 5^1
3 3 × 5 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: 127, 3, 5
3
3
×
5
1
×
12
7
1
=
17145
3^3 × 5^1 × 127^1 = 17145
3 3 × 5 1 × 12 7 1 = 17145
Through this we see that the LCM of 127 and 135 is 17145.
How to Find the LCM of 127 and 135 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 127 and 135 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, 127 and 135:
What are the Multiples of 127?
What are the Multiples of 135?
Let’s take a look at the first 10 multiples for each of these numbers, 127 and 135:
First 10 Multiples of 127: 127, 254, 381, 508, 635, 762, 889, 1016, 1143, 1270
First 10 Multiples of 135: 135, 270, 405, 540, 675, 810, 945, 1080, 1215, 1350
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 127 and 135 are 17145, 34290, 51435. Because 17145 is the smallest, it is the least common multiple.
The LCM of 127 and 135 is 17145.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 18 and 100?
What is the LCM of 38 and 67?
What is the LCM of 97 and 123?
What is the LCM of 86 and 80?
What is the LCM of 14 and 130?