Solution: The LCM of 71 and 110 is 7810
Methods
How to find the LCM of 71 and 110 using Prime Factorization
One way to find the LCM of 71 and 110 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 71?
What are the Factors of 110?
Here is the prime factorization of 71:
7
1
1
71^1
7 1 1
And this is the prime factorization of 110:
2
1
×
5
1
×
1
1
1
2^1 × 5^1 × 11^1
2 1 × 5 1 × 1 1 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: 71, 2, 5, 11
2
1
×
5
1
×
1
1
1
×
7
1
1
=
7810
2^1 × 5^1 × 11^1 × 71^1 = 7810
2 1 × 5 1 × 1 1 1 × 7 1 1 = 7810
Through this we see that the LCM of 71 and 110 is 7810.
How to Find the LCM of 71 and 110 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 71 and 110 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, 71 and 110:
What are the Multiples of 71?
What are the Multiples of 110?
Let’s take a look at the first 10 multiples for each of these numbers, 71 and 110:
First 10 Multiples of 71: 71, 142, 213, 284, 355, 426, 497, 568, 639, 710
First 10 Multiples of 110: 110, 220, 330, 440, 550, 660, 770, 880, 990, 1100
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 71 and 110 are 7810, 15620, 23430. Because 7810 is the smallest, it is the least common multiple.
The LCM of 71 and 110 is 7810.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 76 and 35?
What is the LCM of 2 and 38?
What is the LCM of 21 and 126?
What is the LCM of 84 and 99?
What is the LCM of 101 and 136?