LCM of 405 and 413
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 405 and 413 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 167265 as output. Here you can check the answer for Find the LCM of 405 and 413.
What is LCM of 405 and 413
Given Numbers are 405, 413
We can find the LCM of 405, 413 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 405 and 413
Multiples of 405 =405,810,1215,1620,2025,2430,2835,3240,3645,4050,4455,4860,5265,5670,6075,6480,6885,
Multiples of 413 =413,826,1239,1652,2065,2478,2891,3304,3717,4130,4543,4956,5369,5782,6195,6608,7021,
Now, get the least common multiple of 405, 413 which is 167265
So, the LCM of 405, 413 is 167265.
Least Common Multiple (LCM) of 405 and 413 with the help of Prime Factorisation
One method for determining the LCM of 405 and 413 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 413's prime factorization:
| 7 | 413 |
| 59 | 59 |
| 1 |
Prime factors of 413 are 7,59.
413 = 71×591
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, 7,59
.34×51×71×591 = 167265
This shows that the LCM of 405 and 413 is 167265.
How to Calculate the LCM of 405 and 413 Using Common Multiples
The first step in determining the Least Common Multiple of 405 and 413 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 405 and 413:
Lets look at the first ten multiples of these numbers, 405 and 413:
405,810,1215,1620,2025,2430,2835,3240,3645,6885 are the first ten multiples of 405.
413,826,1239,1652,2065,2478,2891,3304,3717,7021 are the first ten multiples of 413.
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 413, for example, are 4860, 6885, and 6608. 167265 is the least common multiple since it is the smallest.
405 and 413 have an LCM of 167265.
Least Common Multiple of 405 and 413 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 413, than apply into the LCM equation.
GCF(405,413) = 1
LCM(405,413) = ( 405 × 413) / 1
LCM(405,413) = 167265 / 1
LCM(405,413) = 167265
Related Least Common Multiples of 405
Related Least Common Multiples of 413
Frequently Asked Questions on LCM of 405 and 413
1. What is the LCM of 405 and 413?
The LCM of 405 and 413 is 167265.
2. How to find the lowest common multiple of 405 and 413?
To find the lowest common multiple of 405 and 413, we have to get the multip;es of both numbers and identify the least common multiple in them which is 167265.
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 413?
Answer: Factors of 413 are 1, 7, 59, 413. There are 4 integers that are factors of 413. The greatest factor of 413 is 413.
5. How to Find the LCM of 405 and 413?Answer:
Least Common Multiple of 405 and 413 = 167265
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 413
413 = 7 x 59
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 167265 = 3 x 3 x 3 x 3 x 5 x 7 x 59
Step 4: Therefore, the least common multiple of 405 and 413 is 167265.