MATH SOLVE

1 month ago

Q:
# What is the LCM of 148 and 31?

Accepted Solution

A:

Solution: The LCM of 148 and 31 is 4588
Methods
How to find the LCM of 148 and 31 using Prime Factorization
One way to find the LCM of 148 and 31 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 148?
What are the Factors of 31?
Here is the prime factorization of 148:
2
2
×
3
7
1
2^2 × 37^1
2 2 × 3 7 1
And this is the prime factorization of 31:
3
1
1
31^1
3 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: 2, 37, 31
2
2
×
3
1
1
×
3
7
1
=
4588
2^2 × 31^1 × 37^1 = 4588
2 2 × 3 1 1 × 3 7 1 = 4588
Through this we see that the LCM of 148 and 31 is 4588.
How to Find the LCM of 148 and 31 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 148 and 31 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, 148 and 31:
What are the Multiples of 148?
What are the Multiples of 31?
Let’s take a look at the first 10 multiples for each of these numbers, 148 and 31:
First 10 Multiples of 148: 148, 296, 444, 592, 740, 888, 1036, 1184, 1332, 1480
First 10 Multiples of 31: 31, 62, 93, 124, 155, 186, 217, 248, 279, 310
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 148 and 31 are 4588, 9176, 13764. Because 4588 is the smallest, it is the least common multiple.
The LCM of 148 and 31 is 4588.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 71 and 77?
What is the LCM of 19 and 88?
What is the LCM of 91 and 139?
What is the LCM of 39 and 137?
What is the LCM of 102 and 100?