Solution: The LCM of 74 and 140 is 5180
Methods
How to find the LCM of 74 and 140 using Prime Factorization
One way to find the LCM of 74 and 140 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 140?
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 140:
2
2
×
5
1
×
7
1
2^2 × 5^1 × 7^1
2 2 × 5 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, 37, 5, 7
2
2
×
5
1
×
7
1
×
3
7
1
=
5180
2^2 × 5^1 × 7^1 × 37^1 = 5180
2 2 × 5 1 × 7 1 × 3 7 1 = 5180
Through this we see that the LCM of 74 and 140 is 5180.
How to Find the LCM of 74 and 140 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 74 and 140 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 140:
What are the Multiples of 74?
What are the Multiples of 140?
Let’s take a look at the first 10 multiples for each of these numbers, 74 and 140:
First 10 Multiples of 74: 74, 148, 222, 296, 370, 444, 518, 592, 666, 740
First 10 Multiples of 140: 140, 280, 420, 560, 700, 840, 980, 1120, 1260, 1400
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 140 are 5180, 10360, 15540. Because 5180 is the smallest, it is the least common multiple.
The LCM of 74 and 140 is 5180.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 4 and 97?
What is the LCM of 104 and 124?
What is the LCM of 148 and 117?
What is the LCM of 72 and 90?
What is the LCM of 22 and 85?