LCM of 20 and 18
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 20 and 18 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 180 as output. Here you can check the answer for Find the LCM of 20 and 18.
What is LCM of 20 and 18
Given Numbers are 20, 18
We can find the LCM of 20, 18 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 20 and 18
Multiples of 20 =20,40,60,80,100,120,140,160,180,200,220,240,260,280,300,320,340,
Multiples of 18 =18,36,54,72,90,108,126,144,162,180,198,216,234,252,270,288,306,
Now, get the least common multiple of 20, 18 which is 180
So, the LCM of 20, 18 is 180.
Least Common Multiple (LCM) of 20 and 18 with the help of Prime Factorisation
One method for determining the LCM of 20 and 18 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 18's prime factorization:
| 2 | 18 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 18 are 2,3.
18 = 21×32
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
.22×32×51 = 180
This shows that the LCM of 20 and 18 is 180.
How to Calculate the LCM of 20 and 18 Using Common Multiples
The first step in determining the Least Common Multiple of 20 and 18 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 20 and 18:
Lets look at the first ten multiples of these numbers, 20 and 18:
20,40,60,80,100,120,140,160,180,340 are the first ten multiples of 20.
18,36,54,72,90,108,126,144,162,306 are the first ten multiples of 18.
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 18, for example, are 240, 340, and 288. 180 is the least common multiple since it is the smallest.
20 and 18 have an LCM of 180.
Least Common Multiple of 20 and 18 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 18, than apply into the LCM equation.
GCF(20,18) = 2
LCM(20,18) = ( 20 × 18) / 2
LCM(20,18) = 360 / 2
LCM(20,18) = 180
Related Least Common Multiples of 20
Related Least Common Multiples of 18
Frequently Asked Questions on LCM of 20 and 18
1. What is the LCM of 20 and 18?
The LCM of 20 and 18 is 180.
2. How to find the lowest common multiple of 20 and 18?
To find the lowest common multiple of 20 and 18, we have to get the multip;es of both numbers and identify the least common multiple in them which is 180.
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 18?
Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.
5. How to Find the LCM of 20 and 18?Answer:
Least Common Multiple of 20 and 18 = 180
Step 1: Find the prime factorization of 20
20 = 2 x 2 x 5
Step 2: Find the prime factorization of 18
18 = 2 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 = 180 = 2 x 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 20 and 18 is 180.