LCM of 403 and 407
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 403 and 407 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 164021 as output. Here you can check the answer for Find the LCM of 403 and 407.
What is LCM of 403 and 407
Given Numbers are 403, 407
We can find the LCM of 403, 407 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 403 and 407
Multiples of 403 =403,806,1209,1612,2015,2418,2821,3224,3627,4030,4433,4836,5239,5642,6045,6448,6851,
Multiples of 407 =407,814,1221,1628,2035,2442,2849,3256,3663,4070,4477,4884,5291,5698,6105,6512,6919,
Now, get the least common multiple of 403, 407 which is 164021
So, the LCM of 403, 407 is 164021.
Least Common Multiple (LCM) of 403 and 407 with the help of Prime Factorisation
One method for determining the LCM of 403 and 407 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 403's prime factorization:
| 13 | 403 |
| 31 | 31 |
| 1 |
Prime factors of 403 are 13,31.
403 = 131×311
And this is 407's prime factorization:
| 11 | 407 |
| 37 | 37 |
| 1 |
Prime factors of 407 are 11,37.
407 = 111×371
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: 13,31, 11,37
.111×131×311×371 = 164021
This shows that the LCM of 403 and 407 is 164021.
How to Calculate the LCM of 403 and 407 Using Common Multiples
The first step in determining the Least Common Multiple of 403 and 407 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 403 and 407:
Lets look at the first ten multiples of these numbers, 403 and 407:
403,806,1209,1612,2015,2418,2821,3224,3627,6851 are the first ten multiples of 403.
407,814,1221,1628,2035,2442,2849,3256,3663,6919 are the first ten multiples of 407.
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 403 and 407, for example, are 4836, 6851, and 6512. 164021 is the least common multiple since it is the smallest.
403 and 407 have an LCM of 164021.
Least Common Multiple of 403 and 407 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 403 and 407, than apply into the LCM equation.
GCF(403,407) = 1
LCM(403,407) = ( 403 × 407) / 1
LCM(403,407) = 164021 / 1
LCM(403,407) = 164021
Related Least Common Multiples of 403
Related Least Common Multiples of 407
Frequently Asked Questions on LCM of 403 and 407
1. What is the LCM of 403 and 407?
The LCM of 403 and 407 is 164021.
2. How to find the lowest common multiple of 403 and 407?
To find the lowest common multiple of 403 and 407, we have to get the multip;es of both numbers and identify the least common multiple in them which is 164021.
3. What are the Factors of 403?
Answer: Factors of 403 are 1, 13, 31, 403. There are 4 integers that are factors of 403. The greatest factor of 403 is 403.
4. What are the Factors of 407?
Answer: Factors of 407 are 1, 11, 37, 407. There are 4 integers that are factors of 407. The greatest factor of 407 is 407.
5. How to Find the LCM of 403 and 407?Answer:
Least Common Multiple of 403 and 407 = 164021
Step 1: Find the prime factorization of 403
403 = 13 x 31
Step 2: Find the prime factorization of 407
407 = 11 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 164021 = 11 x 13 x 31 x 37
Step 4: Therefore, the least common multiple of 403 and 407 is 164021.