Solution: The LCM of 35 and 103 is 3605
Methods
How to find the LCM of 35 and 103 using Prime Factorization
One way to find the LCM of 35 and 103 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 35?
What are the Factors of 103?
Here is the prime factorization of 35:
5
1
×
7
1
5^1 × 7^1
5 1 × 7 1
And this is the prime factorization of 103:
10
3
1
103^1
10 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: 5, 7, 103
5
1
×
7
1
×
10
3
1
=
3605
5^1 × 7^1 × 103^1 = 3605
5 1 × 7 1 × 10 3 1 = 3605
Through this we see that the LCM of 35 and 103 is 3605.
How to Find the LCM of 35 and 103 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 35 and 103 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, 35 and 103:
What are the Multiples of 35?
What are the Multiples of 103?
Let’s take a look at the first 10 multiples for each of these numbers, 35 and 103:
First 10 Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350
First 10 Multiples of 103: 103, 206, 309, 412, 515, 618, 721, 824, 927, 1030
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 35 and 103 are 3605, 7210, 10815. Because 3605 is the smallest, it is the least common multiple.
The LCM of 35 and 103 is 3605.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 30 and 34?
What is the LCM of 46 and 141?
What is the LCM of 116 and 43?
What is the LCM of 149 and 40?
What is the LCM of 107 and 124?