Solution: The LCM of 74 and 44 is 1628
Methods
How to find the LCM of 74 and 44 using Prime Factorization
One way to find the LCM of 74 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 74?
What are the Factors of 44?
Here is the prime factorization of 74:
2
1
×
3
7
1
2^1 × 37^1
2 1 × 3 7 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: 2, 37, 11
2
2
×
1
1
1
×
3
7
1
=
1628
2^2 × 11^1 × 37^1 = 1628
2 2 × 1 1 1 × 3 7 1 = 1628
Through this we see that the LCM of 74 and 44 is 1628.
How to Find the LCM of 74 and 44 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 74 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, 74 and 44:
What are the Multiples of 74?
What are the Multiples of 44?
Let’s take a look at the first 10 multiples for each of these numbers, 74 and 44:
First 10 Multiples of 74: 74, 148, 222, 296, 370, 444, 518, 592, 666, 740
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 74 and 44 are 1628, 3256, 4884. Because 1628 is the smallest, it is the least common multiple.
The LCM of 74 and 44 is 1628.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 130 and 21?
What is the LCM of 103 and 148?
What is the LCM of 4 and 71?
What is the LCM of 111 and 145?
What is the LCM of 22 and 124?