Solution: The LCM of 44 and 51 is 2244
Methods
How to find the LCM of 44 and 51 using Prime Factorization
One way to find the LCM of 44 and 51 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 44?
What are the Factors of 51?
Here is the prime factorization of 44:
2
2
×
1
1
1
2^2 × 11^1
2 2 × 1 1 1
And this is the prime factorization of 51:
3
1
×
1
7
1
3^1 × 17^1
3 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, 11, 3, 17
2
2
×
3
1
×
1
1
1
×
1
7
1
=
2244
2^2 × 3^1 × 11^1 × 17^1 = 2244
2 2 × 3 1 × 1 1 1 × 1 7 1 = 2244
Through this we see that the LCM of 44 and 51 is 2244.
How to Find the LCM of 44 and 51 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 44 and 51 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, 44 and 51:
What are the Multiples of 44?
What are the Multiples of 51?
Let’s take a look at the first 10 multiples for each of these numbers, 44 and 51:
First 10 Multiples of 44: 44, 88, 132, 176, 220, 264, 308, 352, 396, 440
First 10 Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, 510
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 44 and 51 are 2244, 4488, 6732. Because 2244 is the smallest, it is the least common multiple.
The LCM of 44 and 51 is 2244.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 56 and 71?
What is the LCM of 121 and 110?
What is the LCM of 49 and 42?
What is the LCM of 55 and 117?
What is the LCM of 104 and 147?