LCM of 20 and 27
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 20 and 27 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 540 as output. Here you can check the answer for Find the LCM of 20 and 27.
What is LCM of 20 and 27
Given Numbers are 20, 27
We can find the LCM of 20, 27 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 20 and 27
Multiples of 20 =20,40,60,80,100,120,140,160,180,200,220,240,260,280,300,320,340,
Multiples of 27 =27,54,81,108,135,162,189,216,243,270,297,324,351,378,405,432,459,
Now, get the least common multiple of 20, 27 which is 540
So, the LCM of 20, 27 is 540.
Least Common Multiple (LCM) of 20 and 27 with the help of Prime Factorisation
One method for determining the LCM of 20 and 27 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 20's prime factorization:
| 2 | 20 |
| 2 | 10 |
| 5 | 5 |
| 1 |
Prime factors of 20 are 2,5.
20 = 22×51
And this is 27's prime factorization:
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 27 are 3.
27 = 33
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: 2,5,3
.22×33×51 = 540
This shows that the LCM of 20 and 27 is 540.
How to Calculate the LCM of 20 and 27 Using Common Multiples
The first step in determining the Least Common Multiple of 20 and 27 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 20 and 27:
Lets look at the first ten multiples of these numbers, 20 and 27:
20,40,60,80,100,120,140,160,180,340 are the first ten multiples of 20.
27,54,81,108,135,162,189,216,243,459 are the first ten multiples of 27.
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 20 and 27, for example, are 240, 340, and 432. 540 is the least common multiple since it is the smallest.
20 and 27 have an LCM of 540.
Least Common Multiple of 20 and 27 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20 and 27, than apply into the LCM equation.
GCF(20,27) = 1
LCM(20,27) = ( 20 × 27) / 1
LCM(20,27) = 540 / 1
LCM(20,27) = 540
Related Least Common Multiples of 20
Related Least Common Multiples of 27
Frequently Asked Questions on LCM of 20 and 27
1. What is the LCM of 20 and 27?
The LCM of 20 and 27 is 540.
2. How to find the lowest common multiple of 20 and 27?
To find the lowest common multiple of 20 and 27, we have to get the multip;es of both numbers and identify the least common multiple in them which is 540.
3. What are the Factors of 20?
Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.
4. What are the Factors of 27?
Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.
5. How to Find the LCM of 20 and 27?Answer:
Least Common Multiple of 20 and 27 = 540
Step 1: Find the prime factorization of 20
20 = 2 x 2 x 5
Step 2: Find the prime factorization of 27
27 = 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 540 = 2 x 2 x 3 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 20 and 27 is 540.