Solution: The LCM of 69 and 134 is 9246
Methods
How to find the LCM of 69 and 134 using Prime Factorization
One way to find the LCM of 69 and 134 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 69?
What are the Factors of 134?
Here is the prime factorization of 69:
3
1
×
2
3
1
3^1 × 23^1
3 1 × 2 3 1
And this is the prime factorization of 134:
2
1
×
6
7
1
2^1 × 67^1
2 1 × 6 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, 23, 2, 67
2
1
×
3
1
×
2
3
1
×
6
7
1
=
9246
2^1 × 3^1 × 23^1 × 67^1 = 9246
2 1 × 3 1 × 2 3 1 × 6 7 1 = 9246
Through this we see that the LCM of 69 and 134 is 9246.
How to Find the LCM of 69 and 134 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 69 and 134 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, 69 and 134:
What are the Multiples of 69?
What are the Multiples of 134?
Let’s take a look at the first 10 multiples for each of these numbers, 69 and 134:
First 10 Multiples of 69: 69, 138, 207, 276, 345, 414, 483, 552, 621, 690
First 10 Multiples of 134: 134, 268, 402, 536, 670, 804, 938, 1072, 1206, 1340
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 69 and 134 are 9246, 18492, 27738. Because 9246 is the smallest, it is the least common multiple.
The LCM of 69 and 134 is 9246.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 48 and 2?
What is the LCM of 50 and 37?
What is the LCM of 60 and 70?
What is the LCM of 147 and 149?
What is the LCM of 4 and 96?