Solution: The LCM of 23 and 35 is 805
Methods
How to find the LCM of 23 and 35 using Prime Factorization
One way to find the LCM of 23 and 35 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 23?
What are the Factors of 35?
Here is the prime factorization of 23:
2
3
1
23^1
2 3 1
And this is the prime factorization of 35:
5
1
×
7
1
5^1 × 7^1
5 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: 23, 5, 7
5
1
×
7
1
×
2
3
1
=
805
5^1 × 7^1 × 23^1 = 805
5 1 × 7 1 × 2 3 1 = 805
Through this we see that the LCM of 23 and 35 is 805.
How to Find the LCM of 23 and 35 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 23 and 35 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, 23 and 35:
What are the Multiples of 23?
What are the Multiples of 35?
Let’s take a look at the first 10 multiples for each of these numbers, 23 and 35:
First 10 Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, 230
First 10 Multiples of 35: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350
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 23 and 35 are 805, 1610, 2415. Because 805 is the smallest, it is the least common multiple.
The LCM of 23 and 35 is 805.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 42 and 15?
What is the LCM of 45 and 66?
What is the LCM of 130 and 110?
What is the LCM of 50 and 138?
What is the LCM of 12 and 77?