Solution: The LCM of 45 and 102 is 1530
Methods
How to find the LCM of 45 and 102 using Prime Factorization
One way to find the LCM of 45 and 102 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 45?
What are the Factors of 102?
Here is the prime factorization of 45:
3
2
×
5
1
3^2 × 5^1
3 2 × 5 1
And this is the prime factorization of 102:
2
1
×
3
1
×
1
7
1
2^1 × 3^1 × 17^1
2 1 × 3 1 × 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: 3, 5, 2, 17
2
1
×
3
2
×
5
1
×
1
7
1
=
1530
2^1 × 3^2 × 5^1 × 17^1 = 1530
2 1 × 3 2 × 5 1 × 1 7 1 = 1530
Through this we see that the LCM of 45 and 102 is 1530.
How to Find the LCM of 45 and 102 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 45 and 102 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, 45 and 102:
What are the Multiples of 45?
What are the Multiples of 102?
Let’s take a look at the first 10 multiples for each of these numbers, 45 and 102:
First 10 Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450
First 10 Multiples of 102: 102, 204, 306, 408, 510, 612, 714, 816, 918, 1020
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 45 and 102 are 1530, 3060, 4590. Because 1530 is the smallest, it is the least common multiple.
The LCM of 45 and 102 is 1530.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 64 and 61?
What is the LCM of 69 and 41?
What is the LCM of 68 and 123?
What is the LCM of 3 and 113?
What is the LCM of 13 and 88?