LCM of 24 and 31
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 24 and 31 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 744 as output. Here you can check the answer for Find the LCM of 24 and 31.
What is LCM of 24 and 31
Given Numbers are 24, 31
We can find the LCM of 24, 31 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 24 and 31
Multiples of 24 =24,48,72,96,120,144,168,192,216,240,264,288,312,336,360,384,408,
Multiples of 31 =31,62,93,124,155,186,217,248,279,310,341,372,403,434,465,496,527,
Now, get the least common multiple of 24, 31 which is 744
So, the LCM of 24, 31 is 744.
Least Common Multiple (LCM) of 24 and 31 with the help of Prime Factorisation
One method for determining the LCM of 24 and 31 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:
Here is 24's prime factorization:
| 2 | 24 |
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 24 are 2,3.
24 = 23×31
And this is 31's prime factorization:
| 31 | 31 |
| 1 |
Prime factors of 31 are 31.
31 = 311
When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 2,3,31
.23×31×311 = 744
This shows that the LCM of 24 and 31 is 744.
How to Calculate the LCM of 24 and 31 Using Common Multiples
The first step in determining the Least Common Multiple of 24 and 31 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 24 and 31:
Lets look at the first ten multiples of these numbers, 24 and 31:
24,48,72,96,120,144,168,192,216,408 are the first ten multiples of 24.
31,62,93,124,155,186,217,248,279,527 are the first ten multiples of 31.
You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 24 and 31, for example, are 288, 408, and 496. 744 is the least common multiple since it is the smallest.
24 and 31 have an LCM of 744.
Least Common Multiple of 24 and 31 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 24 and 31, than apply into the LCM equation.
GCF(24,31) = 1
LCM(24,31) = ( 24 × 31) / 1
LCM(24,31) = 744 / 1
LCM(24,31) = 744
Related Least Common Multiples of 24
Related Least Common Multiples of 31
Frequently Asked Questions on LCM of 24 and 31
1. What is the LCM of 24 and 31?
The LCM of 24 and 31 is 744.
2. How to find the lowest common multiple of 24 and 31?
To find the lowest common multiple of 24 and 31, we have to get the multip;es of both numbers and identify the least common multiple in them which is 744.
3. What are the Factors of 24?
Answer: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. There are 8 integers that are factors of 24. The greatest factor of 24 is 24.
4. What are the Factors of 31?
Answer: Factors of 31 are 1, 31. There are 2 integers that are factors of 31. The greatest factor of 31 is 31.
5. How to Find the LCM of 24 and 31?Answer:
Least Common Multiple of 24 and 31 = 744
Step 1: Find the prime factorization of 24
24 = 2 x 2 x 2 x 3
Step 2: Find the prime factorization of 31
31 = 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 744 = 2 x 2 x 2 x 3 x 31
Step 4: Therefore, the least common multiple of 24 and 31 is 744.