LCM of 200 and 204
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 200 and 204 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 10200 as output. Here you can check the answer for Find the LCM of 200 and 204.
What is LCM of 200 and 204
Given Numbers are 200, 204
We can find the LCM of 200, 204 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 200 and 204
Multiples of 200 =200,400,600,800,1000,1200,1400,1600,1800,2000,2200,2400,2600,2800,3000,3200,3400,
Multiples of 204 =204,408,612,816,1020,1224,1428,1632,1836,2040,2244,2448,2652,2856,3060,3264,3468,
Now, get the least common multiple of 200, 204 which is 10200
So, the LCM of 200, 204 is 10200.
Least Common Multiple (LCM) of 200 and 204 with the help of Prime Factorisation
One method for determining the LCM of 200 and 204 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 200's prime factorization:
| 2 | 200 |
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 200 are 2,5.
200 = 23×52
And this is 204's prime factorization:
| 2 | 204 |
| 2 | 102 |
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 204 are 2, 3,17.
204 = 22×31×171
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, 3,17
.23×31×52×171 = 10200
This shows that the LCM of 200 and 204 is 10200.
How to Calculate the LCM of 200 and 204 Using Common Multiples
The first step in determining the Least Common Multiple of 200 and 204 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 200 and 204:
Lets look at the first ten multiples of these numbers, 200 and 204:
200,400,600,800,1000,1200,1400,1600,1800,3400 are the first ten multiples of 200.
204,408,612,816,1020,1224,1428,1632,1836,3468 are the first ten multiples of 204.
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 200 and 204, for example, are 2400, 3400, and 3264. 10200 is the least common multiple since it is the smallest.
200 and 204 have an LCM of 10200.
Least Common Multiple of 200 and 204 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 200 and 204, than apply into the LCM equation.
GCF(200,204) = 4
LCM(200,204) = ( 200 × 204) / 4
LCM(200,204) = 40800 / 4
LCM(200,204) = 10200
Related Least Common Multiples of 200
Related Least Common Multiples of 204
Frequently Asked Questions on LCM of 200 and 204
1. What is the LCM of 200 and 204?
The LCM of 200 and 204 is 10200.
2. How to find the lowest common multiple of 200 and 204?
To find the lowest common multiple of 200 and 204, we have to get the multip;es of both numbers and identify the least common multiple in them which is 10200.
3. What are the Factors of 200?
Answer: Factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200. There are 12 integers that are factors of 200. The greatest factor of 200 is 200.
4. What are the Factors of 204?
Answer: Factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204. There are 12 integers that are factors of 204. The greatest factor of 204 is 204.
5. How to Find the LCM of 200 and 204?Answer:
Least Common Multiple of 200 and 204 = 10200
Step 1: Find the prime factorization of 200
200 = 2 x 2 x 2 x 5 x 5
Step 2: Find the prime factorization of 204
204 = 2 x 2 x 3 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 10200 = 2 x 2 x 2 x 3 x 5 x 5 x 17
Step 4: Therefore, the least common multiple of 200 and 204 is 10200.