Solution: The LCM of 123 and 44 is 5412
Methods
How to find the LCM of 123 and 44 using Prime Factorization
One way to find the LCM of 123 and 44 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 123?
What are the Factors of 44?
Here is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 1
And this is the prime factorization of 44:
2
2
×
1
1
1
2^2 × 11^1
2 2 × 1 1 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: 3, 41, 2, 11
2
2
×
3
1
×
1
1
1
×
4
1
1
=
5412
2^2 × 3^1 × 11^1 × 41^1 = 5412
2 2 × 3 1 × 1 1 1 × 4 1 1 = 5412
Through this we see that the LCM of 123 and 44 is 5412.
How to Find the LCM of 123 and 44 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 123 and 44 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, 123 and 44:
What are the Multiples of 123?
What are the Multiples of 44?
Let’s take a look at the first 10 multiples for each of these numbers, 123 and 44:
First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230
First 10 Multiples of 44: 44, 88, 132, 176, 220, 264, 308, 352, 396, 440
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 123 and 44 are 5412, 10824, 16236. Because 5412 is the smallest, it is the least common multiple.
The LCM of 123 and 44 is 5412.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 86 and 90?
What is the LCM of 42 and 38?
What is the LCM of 132 and 87?
What is the LCM of 41 and 37?
What is the LCM of 19 and 10?