Solution: The LCM of 74 and 42 is 1554
Methods
How to find the LCM of 74 and 42 using Prime Factorization
One way to find the LCM of 74 and 42 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 42?
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 42:
2
1
×
3
1
×
7
1
2^1 × 3^1 × 7^1
2 1 × 3 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, 3, 7
2
1
×
3
1
×
7
1
×
3
7
1
=
1554
2^1 × 3^1 × 7^1 × 37^1 = 1554
2 1 × 3 1 × 7 1 × 3 7 1 = 1554
Through this we see that the LCM of 74 and 42 is 1554.
How to Find the LCM of 74 and 42 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 74 and 42 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 42:
What are the Multiples of 74?
What are the Multiples of 42?
Let’s take a look at the first 10 multiples for each of these numbers, 74 and 42:
First 10 Multiples of 74: 74, 148, 222, 296, 370, 444, 518, 592, 666, 740
First 10 Multiples of 42: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420
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 42 are 1554, 3108, 4662. Because 1554 is the smallest, it is the least common multiple.
The LCM of 74 and 42 is 1554.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 56 and 30?
What is the LCM of 13 and 78?
What is the LCM of 65 and 132?
What is the LCM of 14 and 40?
What is the LCM of 119 and 116?