LCM of 24 and 28
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 24 and 28 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 168 as output. Here you can check the answer for Find the LCM of 24 and 28.
What is LCM of 24 and 28
Given Numbers are 24, 28
We can find the LCM of 24, 28 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 24 and 28
Multiples of 24 =24,48,72,96,120,144,168,192,216,240,264,288,312,336,360,384,408,
Multiples of 28 =28,56,84,112,140,168,196,224,252,280,308,336,364,392,420,448,476,
Now, get the least common multiple of 24, 28 which is 168
So, the LCM of 24, 28 is 168.
Least Common Multiple (LCM) of 24 and 28 with the help of Prime Factorisation
One method for determining the LCM of 24 and 28 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 28's prime factorization:
| 2 | 28 |
| 2 | 14 |
| 7 | 7 |
| 1 |
Prime factors of 28 are 2,7.
28 = 22×71
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: 2,3,7
.23×31×71 = 168
This shows that the LCM of 24 and 28 is 168.
How to Calculate the LCM of 24 and 28 Using Common Multiples
The first step in determining the Least Common Multiple of 24 and 28 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 24 and 28:
Lets look at the first ten multiples of these numbers, 24 and 28:
24,48,72,96,120,144,168,192,216,408 are the first ten multiples of 24.
28,56,84,112,140,168,196,224,252,476 are the first ten multiples of 28.
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 28, for example, are 288, 408, and 448. 168 is the least common multiple since it is the smallest.
24 and 28 have an LCM of 168.
Least Common Multiple of 24 and 28 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 28, than apply into the LCM equation.
GCF(24,28) = 4
LCM(24,28) = ( 24 × 28) / 4
LCM(24,28) = 672 / 4
LCM(24,28) = 168
Related Least Common Multiples of 24
Related Least Common Multiples of 28
Frequently Asked Questions on LCM of 24 and 28
1. What is the LCM of 24 and 28?
The LCM of 24 and 28 is 168.
2. How to find the lowest common multiple of 24 and 28?
To find the lowest common multiple of 24 and 28, we have to get the multip;es of both numbers and identify the least common multiple in them which is 168.
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 28?
Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.
5. How to Find the LCM of 24 and 28?Answer:
Least Common Multiple of 24 and 28 = 168
Step 1: Find the prime factorization of 24
24 = 2 x 2 x 2 x 3
Step 2: Find the prime factorization of 28
28 = 2 x 2 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 168 = 2 x 2 x 2 x 3 x 7
Step 4: Therefore, the least common multiple of 24 and 28 is 168.