Solution: The LCM of 123 and 21 is 861
Methods
How to find the LCM of 123 and 21 using Prime Factorization
One way to find the LCM of 123 and 21 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 123?
What are the Factors of 21?
Here is the prime factorization of 123:
3
1
×
4
1
1
3^1 × 41^1
3 1 × 4 1 1
And this is the prime factorization of 21:
3
1
×
7
1
3^1 × 7^1
3 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: 3, 41, 7
3
1
×
7
1
×
4
1
1
=
861
3^1 × 7^1 × 41^1 = 861
3 1 × 7 1 × 4 1 1 = 861
Through this we see that the LCM of 123 and 21 is 861.
How to Find the LCM of 123 and 21 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 123 and 21 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, 123 and 21:
What are the Multiples of 123?
What are the Multiples of 21?
Let’s take a look at the first 10 multiples for each of these numbers, 123 and 21:
First 10 Multiples of 123: 123, 246, 369, 492, 615, 738, 861, 984, 1107, 1230
First 10 Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210
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 123 and 21 are 861, 1722, 2583. Because 861 is the smallest, it is the least common multiple.
The LCM of 123 and 21 is 861.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 142 and 54?
What is the LCM of 35 and 2?
What is the LCM of 143 and 62?
What is the LCM of 119 and 110?
What is the LCM of 137 and 105?