Solution: The LCM of 67 and 73 is 4891
Methods
How to find the LCM of 67 and 73 using Prime Factorization
One way to find the LCM of 67 and 73 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 67?
What are the Factors of 73?
Here is the prime factorization of 67:
6
7
1
67^1
6 7 1
And this is the prime factorization of 73:
7
3
1
73^1
7 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: 67, 73
6
7
1
×
7
3
1
=
4891
67^1 × 73^1 = 4891
6 7 1 × 7 3 1 = 4891
Through this we see that the LCM of 67 and 73 is 4891.
How to Find the LCM of 67 and 73 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 67 and 73 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, 67 and 73:
What are the Multiples of 67?
What are the Multiples of 73?
Let’s take a look at the first 10 multiples for each of these numbers, 67 and 73:
First 10 Multiples of 67: 67, 134, 201, 268, 335, 402, 469, 536, 603, 670
First 10 Multiples of 73: 73, 146, 219, 292, 365, 438, 511, 584, 657, 730
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 67 and 73 are 4891, 9782, 14673. Because 4891 is the smallest, it is the least common multiple.
The LCM of 67 and 73 is 4891.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 72 and 100?
What is the LCM of 97 and 83?
What is the LCM of 45 and 109?
What is the LCM of 122 and 39?
What is the LCM of 43 and 137?