LCM of 408 and 414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 408 and 414 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 28152 as output. Here you can check the answer for Find the LCM of 408 and 414.
What is LCM of 408 and 414
Given Numbers are 408, 414
We can find the LCM of 408, 414 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 408 and 414
Multiples of 408 =408,816,1224,1632,2040,2448,2856,3264,3672,4080,4488,4896,5304,5712,6120,6528,6936,
Multiples of 414 =414,828,1242,1656,2070,2484,2898,3312,3726,4140,4554,4968,5382,5796,6210,6624,7038,
Now, get the least common multiple of 408, 414 which is 28152
So, the LCM of 408, 414 is 28152.
Least Common Multiple (LCM) of 408 and 414 with the help of Prime Factorisation
One method for determining the LCM of 408 and 414 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 408's prime factorization:
| 2 | 408 |
| 2 | 204 |
| 2 | 102 |
| 3 | 51 |
| 17 | 17 |
| 1 |
Prime factors of 408 are 2, 3,17.
408 = 23×31×171
And this is 414's prime factorization:
| 2 | 414 |
| 3 | 207 |
| 3 | 69 |
| 23 | 23 |
| 1 |
Prime factors of 414 are 2, 3,23.
414 = 21×32×231
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, 3,17,23
.23×32×171×231 = 28152
This shows that the LCM of 408 and 414 is 28152.
How to Calculate the LCM of 408 and 414 Using Common Multiples
The first step in determining the Least Common Multiple of 408 and 414 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 408 and 414:
Lets look at the first ten multiples of these numbers, 408 and 414:
408,816,1224,1632,2040,2448,2856,3264,3672,6936 are the first ten multiples of 408.
414,828,1242,1656,2070,2484,2898,3312,3726,7038 are the first ten multiples of 414.
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 408 and 414, for example, are 4896, 6936, and 6624. 28152 is the least common multiple since it is the smallest.
408 and 414 have an LCM of 28152.
Least Common Multiple of 408 and 414 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 408 and 414, than apply into the LCM equation.
GCF(408,414) = 6
LCM(408,414) = ( 408 × 414) / 6
LCM(408,414) = 168912 / 6
LCM(408,414) = 28152
Related Least Common Multiples of 408
Related Least Common Multiples of 414
Frequently Asked Questions on LCM of 408 and 414
1. What is the LCM of 408 and 414?
The LCM of 408 and 414 is 28152.
2. How to find the lowest common multiple of 408 and 414?
To find the lowest common multiple of 408 and 414, we have to get the multip;es of both numbers and identify the least common multiple in them which is 28152.
3. What are the Factors of 408?
Answer: Factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408. There are 16 integers that are factors of 408. The greatest factor of 408 is 408.
4. What are the Factors of 414?
Answer: Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414. There are 12 integers that are factors of 414. The greatest factor of 414 is 414.
5. How to Find the LCM of 408 and 414?Answer:
Least Common Multiple of 408 and 414 = 28152
Step 1: Find the prime factorization of 408
408 = 2 x 2 x 2 x 3 x 17
Step 2: Find the prime factorization of 414
414 = 2 x 3 x 3 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 28152 = 2 x 2 x 2 x 3 x 3 x 17 x 23
Step 4: Therefore, the least common multiple of 408 and 414 is 28152.