LCM of 12 and 20
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 12 and 20 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 60 as output. Here you can check the answer for Find the LCM of 12 and 20.
What is LCM of 12 and 20
Given Numbers are 12, 20
We can find the LCM of 12, 20 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 12 and 20
Multiples of 12 =12,24,36,48,60,72,84,96,108,120,132,144,156,168,180,192,204,
Multiples of 20 =20,40,60,80,100,120,140,160,180,200,220,240,260,280,300,320,340,
Now, get the least common multiple of 12, 20 which is 60
So, the LCM of 12, 20 is 60.
Least Common Multiple (LCM) of 12 and 20 with the help of Prime Factorisation
One method for determining the LCM of 12 and 20 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 12's prime factorization:
| 2 | 12 |
| 2 | 6 |
| 3 | 3 |
| 1 |
Prime factors of 12 are 2,3.
12 = 22×31
And this is 20's prime factorization:
| 2 | 20 |
| 2 | 10 |
| 5 | 5 |
| 1 |
Prime factors of 20 are 2,5.
20 = 22×51
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: 2,3,5
.22×31×51 = 60
This shows that the LCM of 12 and 20 is 60.
How to Calculate the LCM of 12 and 20 Using Common Multiples
The first step in determining the Least Common Multiple of 12 and 20 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 12 and 20:
Lets look at the first ten multiples of these numbers, 12 and 20:
12,24,36,48,60,72,84,96,108,204 are the first ten multiples of 12.
20,40,60,80,100,120,140,160,180,340 are the first ten multiples of 20.
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 12 and 20, for example, are 144, 204, and 320. 60 is the least common multiple since it is the smallest.
12 and 20 have an LCM of 60.
Least Common Multiple of 12 and 20 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 20, than apply into the LCM equation.
GCF(12,20) = 4
LCM(12,20) = ( 12 × 20) / 4
LCM(12,20) = 240 / 4
LCM(12,20) = 60
Related Least Common Multiples of 12
Related Least Common Multiples of 20
Frequently Asked Questions on LCM of 12 and 20
1. What is the LCM of 12 and 20?
The LCM of 12 and 20 is 60.
2. How to find the lowest common multiple of 12 and 20?
To find the lowest common multiple of 12 and 20, we have to get the multip;es of both numbers and identify the least common multiple in them which is 60.
3. What are the Factors of 12?
Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.
4. 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.
5. How to Find the LCM of 12 and 20?Answer:
Least Common Multiple of 12 and 20 = 60
Step 1: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 2: Find the prime factorization of 20
20 = 2 x 2 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 60 = 2 x 2 x 3 x 5
Step 4: Therefore, the least common multiple of 12 and 20 is 60.