Solution: The LCM of 16 and 69 is 1104
Methods
How to find the LCM of 16 and 69 using Prime Factorization
One way to find the LCM of 16 and 69 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 16?
What are the Factors of 69?
Here is the prime factorization of 16:
2
4
2^4
2 4
And this is the prime factorization of 69:
3
1
×
2
3
1
3^1 × 23^1
3 1 × 2 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, 23
2
4
×
3
1
×
2
3
1
=
1104
2^4 × 3^1 × 23^1 = 1104
2 4 × 3 1 × 2 3 1 = 1104
Through this we see that the LCM of 16 and 69 is 1104.
How to Find the LCM of 16 and 69 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 16 and 69 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, 16 and 69:
What are the Multiples of 16?
What are the Multiples of 69?
Let’s take a look at the first 10 multiples for each of these numbers, 16 and 69:
First 10 Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160
First 10 Multiples of 69: 69, 138, 207, 276, 345, 414, 483, 552, 621, 690
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 16 and 69 are 1104, 2208, 3312. Because 1104 is the smallest, it is the least common multiple.
The LCM of 16 and 69 is 1104.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 15 and 133?
What is the LCM of 58 and 36?
What is the LCM of 9 and 33?
What is the LCM of 64 and 104?
What is the LCM of 108 and 125?