Solution: The LCM of 46 and 18 is 414
Methods
How to find the LCM of 46 and 18 using Prime Factorization
One way to find the LCM of 46 and 18 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 46?
What are the Factors of 18?
Here is the prime factorization of 46:
2
1
×
2
3
1
2^1 × 23^1
2 1 × 2 3 1
And this is the prime factorization of 18:
2
1
×
3
2
2^1 × 3^2
2 1 × 3 2
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, 23, 3
2
1
×
3
2
×
2
3
1
=
414
2^1 × 3^2 × 23^1 = 414
2 1 × 3 2 × 2 3 1 = 414
Through this we see that the LCM of 46 and 18 is 414.
How to Find the LCM of 46 and 18 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 46 and 18 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, 46 and 18:
What are the Multiples of 46?
What are the Multiples of 18?
Let’s take a look at the first 10 multiples for each of these numbers, 46 and 18:
First 10 Multiples of 46: 46, 92, 138, 184, 230, 276, 322, 368, 414, 460
First 10 Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180
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 46 and 18 are 414, 828, 1242. Because 414 is the smallest, it is the least common multiple.
The LCM of 46 and 18 is 414.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 97 and 84?
What is the LCM of 82 and 59?
What is the LCM of 15 and 37?
What is the LCM of 35 and 103?
What is the LCM of 16 and 99?