LCM of 413 and 417
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 413 and 417 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 172221 as output. Here you can check the answer for Find the LCM of 413 and 417.
What is LCM of 413 and 417
Given Numbers are 413, 417
We can find the LCM of 413, 417 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 413 and 417
Multiples of 413 =413,826,1239,1652,2065,2478,2891,3304,3717,4130,4543,4956,5369,5782,6195,6608,7021,
Multiples of 417 =417,834,1251,1668,2085,2502,2919,3336,3753,4170,4587,5004,5421,5838,6255,6672,7089,
Now, get the least common multiple of 413, 417 which is 172221
So, the LCM of 413, 417 is 172221.
Least Common Multiple (LCM) of 413 and 417 with the help of Prime Factorisation
One method for determining the LCM of 413 and 417 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 413's prime factorization:
| 7 | 413 |
| 59 | 59 |
| 1 |
Prime factors of 413 are 7,59.
413 = 71×591
And this is 417's prime factorization:
| 3 | 417 |
| 139 | 139 |
| 1 |
Prime factors of 417 are 3,139.
417 = 31×1391
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: 7,59, 3,139
.31×71×591×1391 = 172221
This shows that the LCM of 413 and 417 is 172221.
How to Calculate the LCM of 413 and 417 Using Common Multiples
The first step in determining the Least Common Multiple of 413 and 417 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 413 and 417:
Lets look at the first ten multiples of these numbers, 413 and 417:
413,826,1239,1652,2065,2478,2891,3304,3717,7021 are the first ten multiples of 413.
417,834,1251,1668,2085,2502,2919,3336,3753,7089 are the first ten multiples of 417.
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 413 and 417, for example, are 4956, 7021, and 6672. 172221 is the least common multiple since it is the smallest.
413 and 417 have an LCM of 172221.
Least Common Multiple of 413 and 417 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 413 and 417, than apply into the LCM equation.
GCF(413,417) = 1
LCM(413,417) = ( 413 × 417) / 1
LCM(413,417) = 172221 / 1
LCM(413,417) = 172221
Related Least Common Multiples of 413
Related Least Common Multiples of 417
Frequently Asked Questions on LCM of 413 and 417
1. What is the LCM of 413 and 417?
The LCM of 413 and 417 is 172221.
2. How to find the lowest common multiple of 413 and 417?
To find the lowest common multiple of 413 and 417, we have to get the multip;es of both numbers and identify the least common multiple in them which is 172221.
3. 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.
4. What are the Factors of 417?
Answer: Factors of 417 are 1, 3, 139, 417. There are 4 integers that are factors of 417. The greatest factor of 417 is 417.
5. How to Find the LCM of 413 and 417?Answer:
Least Common Multiple of 413 and 417 = 172221
Step 1: Find the prime factorization of 413
413 = 7 x 59
Step 2: Find the prime factorization of 417
417 = 3 x 139
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 172221 = 3 x 7 x 59 x 139
Step 4: Therefore, the least common multiple of 413 and 417 is 172221.