LCM of 21 and 28
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 21 and 28 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 84 as output. Here you can check the answer for Find the LCM of 21 and 28.
What is LCM of 21 and 28
Given Numbers are 21, 28
We can find the LCM of 21, 28 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 21 and 28
Multiples of 21 =21,42,63,84,105,126,147,168,189,210,231,252,273,294,315,336,357,
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 21, 28 which is 84
So, the LCM of 21, 28 is 84.
Least Common Multiple (LCM) of 21 and 28 with the help of Prime Factorisation
One method for determining the LCM of 21 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 21's prime factorization:
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 21 are 3,7.
21 = 31×71
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: 3,7,2
.22×31×71 = 84
This shows that the LCM of 21 and 28 is 84.
How to Calculate the LCM of 21 and 28 Using Common Multiples
The first step in determining the Least Common Multiple of 21 and 28 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 21 and 28:
Lets look at the first ten multiples of these numbers, 21 and 28:
21,42,63,84,105,126,147,168,189,357 are the first ten multiples of 21.
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 21 and 28, for example, are 252, 357, and 448. 84 is the least common multiple since it is the smallest.
21 and 28 have an LCM of 84.
Least Common Multiple of 21 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 21 and 28, than apply into the LCM equation.
GCF(21,28) = 7
LCM(21,28) = ( 21 × 28) / 7
LCM(21,28) = 588 / 7
LCM(21,28) = 84
Related Least Common Multiples of 21
Related Least Common Multiples of 28
Frequently Asked Questions on LCM of 21 and 28
1. What is the LCM of 21 and 28?
The LCM of 21 and 28 is 84.
2. How to find the lowest common multiple of 21 and 28?
To find the lowest common multiple of 21 and 28, we have to get the multip;es of both numbers and identify the least common multiple in them which is 84.
3. What are the Factors of 21?
Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.
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 21 and 28?Answer:
Least Common Multiple of 21 and 28 = 84
Step 1: Find the prime factorization of 21
21 = 3 x 7
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 = 84 = 2 x 2 x 3 x 7
Step 4: Therefore, the least common multiple of 21 and 28 is 84.