LCM of 405 and 410
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 405 and 410 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 33210 as output. Here you can check the answer for Find the LCM of 405 and 410.
What is LCM of 405 and 410
Given Numbers are 405, 410
We can find the LCM of 405, 410 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 405 and 410
Multiples of 405 =405,810,1215,1620,2025,2430,2835,3240,3645,4050,4455,4860,5265,5670,6075,6480,6885,
Multiples of 410 =410,820,1230,1640,2050,2460,2870,3280,3690,4100,4510,4920,5330,5740,6150,6560,6970,
Now, get the least common multiple of 405, 410 which is 33210
So, the LCM of 405, 410 is 33210.
Least Common Multiple (LCM) of 405 and 410 with the help of Prime Factorisation
One method for determining the LCM of 405 and 410 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 410's prime factorization:
| 2 | 410 |
| 5 | 205 |
| 41 | 41 |
| 1 |
Prime factors of 410 are 2, 5,41.
410 = 21×51×411
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, 2,41
.21×34×51×411 = 33210
This shows that the LCM of 405 and 410 is 33210.
How to Calculate the LCM of 405 and 410 Using Common Multiples
The first step in determining the Least Common Multiple of 405 and 410 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 405 and 410:
Lets look at the first ten multiples of these numbers, 405 and 410:
405,810,1215,1620,2025,2430,2835,3240,3645,6885 are the first ten multiples of 405.
410,820,1230,1640,2050,2460,2870,3280,3690,6970 are the first ten multiples of 410.
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 410, for example, are 4860, 6885, and 6560. 33210 is the least common multiple since it is the smallest.
405 and 410 have an LCM of 33210.
Least Common Multiple of 405 and 410 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 410, than apply into the LCM equation.
GCF(405,410) = 5
LCM(405,410) = ( 405 × 410) / 5
LCM(405,410) = 166050 / 5
LCM(405,410) = 33210
Related Least Common Multiples of 405
Related Least Common Multiples of 410
Frequently Asked Questions on LCM of 405 and 410
1. What is the LCM of 405 and 410?
The LCM of 405 and 410 is 33210.
2. How to find the lowest common multiple of 405 and 410?
To find the lowest common multiple of 405 and 410, we have to get the multip;es of both numbers and identify the least common multiple in them which is 33210.
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 410?
Answer: Factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410. There are 8 integers that are factors of 410. The greatest factor of 410 is 410.
5. How to Find the LCM of 405 and 410?Answer:
Least Common Multiple of 405 and 410 = 33210
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 410
410 = 2 x 5 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 33210 = 2 x 3 x 3 x 3 x 3 x 5 x 41
Step 4: Therefore, the least common multiple of 405 and 410 is 33210.