Solution: The LCM of 18 and 146 is 1314
Methods
How to find the LCM of 18 and 146 using Prime Factorization
One way to find the LCM of 18 and 146 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 18?
What are the Factors of 146?
Here is the prime factorization of 18:
2
1
×
3
2
2^1 × 3^2
2 1 × 3 2
And this is the prime factorization of 146:
2
1
×
7
3
1
2^1 × 73^1
2 1 × 7 3 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, 73
2
1
×
3
2
×
7
3
1
=
1314
2^1 × 3^2 × 73^1 = 1314
2 1 × 3 2 × 7 3 1 = 1314
Through this we see that the LCM of 18 and 146 is 1314.
How to Find the LCM of 18 and 146 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 18 and 146 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, 18 and 146:
What are the Multiples of 18?
What are the Multiples of 146?
Let’s take a look at the first 10 multiples for each of these numbers, 18 and 146:
First 10 Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180
First 10 Multiples of 146: 146, 292, 438, 584, 730, 876, 1022, 1168, 1314, 1460
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 18 and 146 are 1314, 2628, 3942. Because 1314 is the smallest, it is the least common multiple.
The LCM of 18 and 146 is 1314.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 138 and 16?
What is the LCM of 85 and 42?
What is the LCM of 112 and 50?
What is the LCM of 128 and 101?
What is the LCM of 102 and 127?