MATH SOLVE

3 months ago

Q:
# What is the LCM of 106 and 58?

Accepted Solution

A:

Solution: The LCM of 106 and 58 is 3074
Methods
How to find the LCM of 106 and 58 using Prime Factorization
One way to find the LCM of 106 and 58 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 106?
What are the Factors of 58?
Here is the prime factorization of 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 3 1
And this is the prime factorization of 58:
2
1
×
2
9
1
2^1 × 29^1
2 1 × 2 9 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, 53, 29
2
1
×
2
9
1
×
5
3
1
=
3074
2^1 × 29^1 × 53^1 = 3074
2 1 × 2 9 1 × 5 3 1 = 3074
Through this we see that the LCM of 106 and 58 is 3074.
How to Find the LCM of 106 and 58 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 106 and 58 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, 106 and 58:
What are the Multiples of 106?
What are the Multiples of 58?
Let’s take a look at the first 10 multiples for each of these numbers, 106 and 58:
First 10 Multiples of 106: 106, 212, 318, 424, 530, 636, 742, 848, 954, 1060
First 10 Multiples of 58: 58, 116, 174, 232, 290, 348, 406, 464, 522, 580
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 106 and 58 are 3074, 6148, 9222. Because 3074 is the smallest, it is the least common multiple.
The LCM of 106 and 58 is 3074.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 29 and 85?
What is the LCM of 59 and 35?
What is the LCM of 127 and 138?
What is the LCM of 77 and 119?
What is the LCM of 46 and 8?