MATH SOLVE

4 months ago

Q:
# What is the LCM of 78 and 23?

Accepted Solution

A:

Solution: The LCM of 78 and 23 is 1794
Methods
How to find the LCM of 78 and 23 using Prime Factorization
One way to find the LCM of 78 and 23 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 78?
What are the Factors of 23?
Here is the prime factorization of 78:
2
1
×
3
1
×
1
3
1
2^1 × 3^1 × 13^1
2 1 × 3 1 × 1 3 1
And this is the prime factorization of 23:
2
3
1
23^1
2 3 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, 3, 13, 23
2
1
×
3
1
×
1
3
1
×
2
3
1
=
1794
2^1 × 3^1 × 13^1 × 23^1 = 1794
2 1 × 3 1 × 1 3 1 × 2 3 1 = 1794
Through this we see that the LCM of 78 and 23 is 1794.
How to Find the LCM of 78 and 23 by Listing Common Multiples
The first step to this method of finding the Least Common Multiple of 78 and 23 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, 78 and 23:
What are the Multiples of 78?
What are the Multiples of 23?
Let’s take a look at the first 10 multiples for each of these numbers, 78 and 23:
First 10 Multiples of 78: 78, 156, 234, 312, 390, 468, 546, 624, 702, 780
First 10 Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, 230
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 78 and 23 are 1794, 3588, 5382. Because 1794 is the smallest, it is the least common multiple.
The LCM of 78 and 23 is 1794.
Find the LCM of Other Number Pairs
Want more practice? Try some of these other LCM problems:
What is the LCM of 65 and 72?
What is the LCM of 84 and 20?
What is the LCM of 102 and 111?
What is the LCM of 108 and 85?
What is the LCM of 49 and 124?