Solution: The LCM of 43 and 102 is 4386
Methods
How to find the LCM of 43 and 102 using Prime Factorization
One way to find the LCM of 43 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 43?
What are the Factors of 102?
Here is the prime factorization of 43:
4
3
1
43^1
4 3 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: 43, 2, 3, 17
2
1
×
3
1
×
1
7
1
×
4
3
1
=
4386
2^1 × 3^1 × 17^1 × 43^1 = 4386
2 1 × 3 1 × 1 7 1 × 4 3 1 = 4386
Through this we see that the LCM of 43 and 102 is 4386.
How to Find the LCM of 43 and 102 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 43 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, 43 and 102:
What are the Multiples of 43?
What are the Multiples of 102?
Let’s take a look at the first 10 multiples for each of these numbers, 43 and 102:
First 10 Multiples of 43: 43, 86, 129, 172, 215, 258, 301, 344, 387, 430
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 43 and 102 are 4386, 8772, 13158. Because 4386 is the smallest, it is the least common multiple.
The LCM of 43 and 102 is 4386.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 44 and 150?
What is the LCM of 116 and 19?
What is the LCM of 7 and 107?
What is the LCM of 17 and 105?
What is the LCM of 86 and 106?