LCM of 26 and 31
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 26 and 31 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 806 as output. Here you can check the answer for Find the LCM of 26 and 31.
What is LCM of 26 and 31
Given Numbers are 26, 31
We can find the LCM of 26, 31 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 26 and 31
Multiples of 26 =26,52,78,104,130,156,182,208,234,260,286,312,338,364,390,416,442,
Multiples of 31 =31,62,93,124,155,186,217,248,279,310,341,372,403,434,465,496,527,
Now, get the least common multiple of 26, 31 which is 806
So, the LCM of 26, 31 is 806.
Least Common Multiple (LCM) of 26 and 31 with the help of Prime Factorisation
One method for determining the LCM of 26 and 31 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 26's prime factorization:
| 2 | 26 |
| 13 | 13 |
| 1 |
Prime factors of 26 are 2,13.
26 = 21×131
And this is 31's prime factorization:
| 31 | 31 |
| 1 |
Prime factors of 31 are 31.
31 = 311
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: 2,13,31
.21×131×311 = 806
This shows that the LCM of 26 and 31 is 806.
How to Calculate the LCM of 26 and 31 Using Common Multiples
The first step in determining the Least Common Multiple of 26 and 31 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 26 and 31:
Lets look at the first ten multiples of these numbers, 26 and 31:
26,52,78,104,130,156,182,208,234,442 are the first ten multiples of 26.
31,62,93,124,155,186,217,248,279,527 are the first ten multiples of 31.
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 26 and 31, for example, are 312, 442, and 496. 806 is the least common multiple since it is the smallest.
26 and 31 have an LCM of 806.
Least Common Multiple of 26 and 31 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 26 and 31, than apply into the LCM equation.
GCF(26,31) = 1
LCM(26,31) = ( 26 × 31) / 1
LCM(26,31) = 806 / 1
LCM(26,31) = 806
Related Least Common Multiples of 26
Related Least Common Multiples of 31
Frequently Asked Questions on LCM of 26 and 31
1. What is the LCM of 26 and 31?
The LCM of 26 and 31 is 806.
2. How to find the lowest common multiple of 26 and 31?
To find the lowest common multiple of 26 and 31, we have to get the multip;es of both numbers and identify the least common multiple in them which is 806.
3. What are the Factors of 26?
Answer: Factors of 26 are 1, 2, 13, 26. There are 4 integers that are factors of 26. The greatest factor of 26 is 26.
4. What are the Factors of 31?
Answer: Factors of 31 are 1, 31. There are 2 integers that are factors of 31. The greatest factor of 31 is 31.
5. How to Find the LCM of 26 and 31?Answer:
Least Common Multiple of 26 and 31 = 806
Step 1: Find the prime factorization of 26
26 = 2 x 13
Step 2: Find the prime factorization of 31
31 = 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 806 = 2 x 13 x 31
Step 4: Therefore, the least common multiple of 26 and 31 is 806.