LCM of 405 and 409
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 405 and 409 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 165645 as output. Here you can check the answer for Find the LCM of 405 and 409.
What is LCM of 405 and 409
Given Numbers are 405, 409
We can find the LCM of 405, 409 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 405 and 409
Multiples of 405 =405,810,1215,1620,2025,2430,2835,3240,3645,4050,4455,4860,5265,5670,6075,6480,6885,
Multiples of 409 =409,818,1227,1636,2045,2454,2863,3272,3681,4090,4499,4908,5317,5726,6135,6544,6953,
Now, get the least common multiple of 405, 409 which is 165645
So, the LCM of 405, 409 is 165645.
Least Common Multiple (LCM) of 405 and 409 with the help of Prime Factorisation
One method for determining the LCM of 405 and 409 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 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
And this is 409's prime factorization:
| 409 | 409 |
| 1 |
Prime factors of 409 are 409.
409 = 4091
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: 3,5,409
.34×51×4091 = 165645
This shows that the LCM of 405 and 409 is 165645.
How to Calculate the LCM of 405 and 409 Using Common Multiples
The first step in determining the Least Common Multiple of 405 and 409 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 405 and 409:
Lets look at the first ten multiples of these numbers, 405 and 409:
405,810,1215,1620,2025,2430,2835,3240,3645,6885 are the first ten multiples of 405.
409,818,1227,1636,2045,2454,2863,3272,3681,6953 are the first ten multiples of 409.
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 405 and 409, for example, are 4860, 6885, and 6544. 165645 is the least common multiple since it is the smallest.
405 and 409 have an LCM of 165645.
Least Common Multiple of 405 and 409 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 405 and 409, than apply into the LCM equation.
GCF(405,409) = 1
LCM(405,409) = ( 405 × 409) / 1
LCM(405,409) = 165645 / 1
LCM(405,409) = 165645
Related Least Common Multiples of 405
Related Least Common Multiples of 409
Frequently Asked Questions on LCM of 405 and 409
1. What is the LCM of 405 and 409?
The LCM of 405 and 409 is 165645.
2. How to find the lowest common multiple of 405 and 409?
To find the lowest common multiple of 405 and 409, we have to get the multip;es of both numbers and identify the least common multiple in them which is 165645.
3. 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.
4. What are the Factors of 409?
Answer: Factors of 409 are 1, 409. There are 2 integers that are factors of 409. The greatest factor of 409 is 409.
5. How to Find the LCM of 405 and 409?Answer:
Least Common Multiple of 405 and 409 = 165645
Step 1: Find the prime factorization of 405
405 = 3 x 3 x 3 x 3 x 5
Step 2: Find the prime factorization of 409
409 = 409
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 165645 = 3 x 3 x 3 x 3 x 5 x 409
Step 4: Therefore, the least common multiple of 405 and 409 is 165645.