LCM of 400 and 405
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 400 and 405 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 32400 as output. Here you can check the answer for Find the LCM of 400 and 405.
What is LCM of 400 and 405
Given Numbers are 400, 405
We can find the LCM of 400, 405 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 400 and 405
Multiples of 400 =400,800,1200,1600,2000,2400,2800,3200,3600,4000,4400,4800,5200,5600,6000,6400,6800,
Multiples of 405 =405,810,1215,1620,2025,2430,2835,3240,3645,4050,4455,4860,5265,5670,6075,6480,6885,
Now, get the least common multiple of 400, 405 which is 32400
So, the LCM of 400, 405 is 32400.
Least Common Multiple (LCM) of 400 and 405 with the help of Prime Factorisation
One method for determining the LCM of 400 and 405 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 400's prime factorization:
| 2 | 400 |
| 2 | 200 |
| 2 | 100 |
| 2 | 50 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 400 are 2,5.
400 = 24×52
And this is 405's prime factorization:
| 3 | 405 |
| 3 | 135 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 405 are 3,5.
405 = 34×51
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: 2,5,3
.24×34×52 = 32400
This shows that the LCM of 400 and 405 is 32400.
How to Calculate the LCM of 400 and 405 Using Common Multiples
The first step in determining the Least Common Multiple of 400 and 405 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 400 and 405:
Lets look at the first ten multiples of these numbers, 400 and 405:
400,800,1200,1600,2000,2400,2800,3200,3600,6800 are the first ten multiples of 400.
405,810,1215,1620,2025,2430,2835,3240,3645,6885 are the first ten multiples of 405.
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 400 and 405, for example, are 4800, 6800, and 6480. 32400 is the least common multiple since it is the smallest.
400 and 405 have an LCM of 32400.
Least Common Multiple of 400 and 405 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 400 and 405, than apply into the LCM equation.
GCF(400,405) = 5
LCM(400,405) = ( 400 × 405) / 5
LCM(400,405) = 162000 / 5
LCM(400,405) = 32400
Related Least Common Multiples of 400
Related Least Common Multiples of 405
Frequently Asked Questions on LCM of 400 and 405
1. What is the LCM of 400 and 405?
The LCM of 400 and 405 is 32400.
2. How to find the lowest common multiple of 400 and 405?
To find the lowest common multiple of 400 and 405, we have to get the multip;es of both numbers and identify the least common multiple in them which is 32400.
3. What are the Factors of 400?
Answer: Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. There are 15 integers that are factors of 400. The greatest factor of 400 is 400.
4. What are the Factors of 405?
Answer: Factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405. There are 10 integers that are factors of 405. The greatest factor of 405 is 405.
5. How to Find the LCM of 400 and 405?Answer:
Least Common Multiple of 400 and 405 = 32400
Step 1: Find the prime factorization of 400
400 = 2 x 2 x 2 x 2 x 5 x 5
Step 2: Find the prime factorization of 405
405 = 3 x 3 x 3 x 3 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 = 32400 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5
Step 4: Therefore, the least common multiple of 400 and 405 is 32400.