Solution: The LCM of 54 and 74 is 1998
Methods
How to find the LCM of 54 and 74 using Prime Factorization
One way to find the LCM of 54 and 74 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 54?
What are the Factors of 74?
Here is the prime factorization of 54:
2
1
×
3
3
2^1 × 3^3
2 1 × 3 3
And this is the prime factorization of 74:
2
1
×
3
7
1
2^1 × 37^1
2 1 × 3 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, 3, 37
2
1
×
3
3
×
3
7
1
=
1998
2^1 × 3^3 × 37^1 = 1998
2 1 × 3 3 × 3 7 1 = 1998
Through this we see that the LCM of 54 and 74 is 1998.
How to Find the LCM of 54 and 74 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 54 and 74 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, 54 and 74:
What are the Multiples of 54?
What are the Multiples of 74?
Let’s take a look at the first 10 multiples for each of these numbers, 54 and 74:
First 10 Multiples of 54: 54, 108, 162, 216, 270, 324, 378, 432, 486, 540
First 10 Multiples of 74: 74, 148, 222, 296, 370, 444, 518, 592, 666, 740
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 54 and 74 are 1998, 3996, 5994. Because 1998 is the smallest, it is the least common multiple.
The LCM of 54 and 74 is 1998.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 125 and 72?
What is the LCM of 20 and 99?
What is the LCM of 30 and 120?
What is the LCM of 15 and 128?
What is the LCM of 106 and 17?