LCM of 108 and 116
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 108 and 116 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 3132 as output. Here you can check the answer for Find the LCM of 108 and 116.
What is LCM of 108 and 116
Given Numbers are 108, 116
We can find the LCM of 108, 116 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 108 and 116
Multiples of 108 =108,216,324,432,540,648,756,864,972,1080,1188,1296,1404,1512,1620,1728,1836,
Multiples of 116 =116,232,348,464,580,696,812,928,1044,1160,1276,1392,1508,1624,1740,1856,1972,
Now, get the least common multiple of 108, 116 which is 3132
So, the LCM of 108, 116 is 3132.
Least Common Multiple (LCM) of 108 and 116 with the help of Prime Factorisation
One method for determining the LCM of 108 and 116 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 108's prime factorization:
| 2 | 108 |
| 2 | 54 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 108 are 2,3.
108 = 22×33
And this is 116's prime factorization:
| 2 | 116 |
| 2 | 58 |
| 29 | 29 |
| 1 |
Prime factors of 116 are 2,29.
116 = 22×291
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: 2,3,29
.22×33×291 = 3132
This shows that the LCM of 108 and 116 is 3132.
How to Calculate the LCM of 108 and 116 Using Common Multiples
The first step in determining the Least Common Multiple of 108 and 116 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 108 and 116:
Lets look at the first ten multiples of these numbers, 108 and 116:
108,216,324,432,540,648,756,864,972,1836 are the first ten multiples of 108.
116,232,348,464,580,696,812,928,1044,1972 are the first ten multiples of 116.
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 108 and 116, for example, are 1296, 1836, and 1856. 3132 is the least common multiple since it is the smallest.
108 and 116 have an LCM of 3132.
Least Common Multiple of 108 and 116 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 108 and 116, than apply into the LCM equation.
GCF(108,116) = 4
LCM(108,116) = ( 108 × 116) / 4
LCM(108,116) = 12528 / 4
LCM(108,116) = 3132
Related Least Common Multiples of 108
Related Least Common Multiples of 116
Frequently Asked Questions on LCM of 108 and 116
1. What is the LCM of 108 and 116?
The LCM of 108 and 116 is 3132.
2. How to find the lowest common multiple of 108 and 116?
To find the lowest common multiple of 108 and 116, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3132.
3. What are the Factors of 108?
Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.
4. What are the Factors of 116?
Answer: Factors of 116 are 1, 2, 4, 29, 58, 116. There are 6 integers that are factors of 116. The greatest factor of 116 is 116.
5. How to Find the LCM of 108 and 116?Answer:
Least Common Multiple of 108 and 116 = 3132
Step 1: Find the prime factorization of 108
108 = 2 x 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 116
116 = 2 x 2 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3132 = 2 x 2 x 3 x 3 x 3 x 29
Step 4: Therefore, the least common multiple of 108 and 116 is 3132.