LCM of 103 and 108
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 103 and 108 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 11124 as output. Here you can check the answer for Find the LCM of 103 and 108.
What is LCM of 103 and 108
Given Numbers are 103, 108
We can find the LCM of 103, 108 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 103 and 108
Multiples of 103 =103,206,309,412,515,618,721,824,927,1030,1133,1236,1339,1442,1545,1648,1751,
Multiples of 108 =108,216,324,432,540,648,756,864,972,1080,1188,1296,1404,1512,1620,1728,1836,
Now, get the least common multiple of 103, 108 which is 11124
So, the LCM of 103, 108 is 11124.
Least Common Multiple (LCM) of 103 and 108 with the help of Prime Factorisation
One method for determining the LCM of 103 and 108 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 103's prime factorization:
| 103 | 103 |
| 1 |
Prime factors of 103 are 103.
103 = 1031
And this 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
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:103, 2,3
.22×33×1031 = 11124
This shows that the LCM of 103 and 108 is 11124.
How to Calculate the LCM of 103 and 108 Using Common Multiples
The first step in determining the Least Common Multiple of 103 and 108 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 103 and 108:
Lets look at the first ten multiples of these numbers, 103 and 108:
103,206,309,412,515,618,721,824,927,1751 are the first ten multiples of 103.
108,216,324,432,540,648,756,864,972,1836 are the first ten multiples of 108.
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 103 and 108, for example, are 1236, 1751, and 1728. 11124 is the least common multiple since it is the smallest.
103 and 108 have an LCM of 11124.
Least Common Multiple of 103 and 108 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 103 and 108, than apply into the LCM equation.
GCF(103,108) = 1
LCM(103,108) = ( 103 × 108) / 1
LCM(103,108) = 11124 / 1
LCM(103,108) = 11124
Related Least Common Multiples of 103
Related Least Common Multiples of 108
Frequently Asked Questions on LCM of 103 and 108
1. What is the LCM of 103 and 108?
The LCM of 103 and 108 is 11124.
2. How to find the lowest common multiple of 103 and 108?
To find the lowest common multiple of 103 and 108, we have to get the multip;es of both numbers and identify the least common multiple in them which is 11124.
3. What are the Factors of 103?
Answer: Factors of 103 are 1, 103. There are 2 integers that are factors of 103. The greatest factor of 103 is 103.
4. 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.
5. How to Find the LCM of 103 and 108?Answer:
Least Common Multiple of 103 and 108 = 11124
Step 1: Find the prime factorization of 103
103 = 103
Step 2: Find the prime factorization of 108
108 = 2 x 2 x 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 11124 = 2 x 2 x 3 x 3 x 3 x 103
Step 4: Therefore, the least common multiple of 103 and 108 is 11124.