LCM of 99 and 103
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 99 and 103 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 10197 as output. Here you can check the answer for Find the LCM of 99 and 103.
What is LCM of 99 and 103
Given Numbers are 99, 103
We can find the LCM of 99, 103 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 99 and 103
Multiples of 99 =99,198,297,396,495,594,693,792,891,990,1089,1188,1287,1386,1485,1584,1683,
Multiples of 103 =103,206,309,412,515,618,721,824,927,1030,1133,1236,1339,1442,1545,1648,1751,
Now, get the least common multiple of 99, 103 which is 10197
So, the LCM of 99, 103 is 10197.
Least Common Multiple (LCM) of 99 and 103 with the help of Prime Factorisation
One method for determining the LCM of 99 and 103 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 99's prime factorization:
| 3 | 99 |
| 3 | 33 |
| 11 | 11 |
| 1 |
Prime factors of 99 are 3,11.
99 = 32×111
And this is 103's prime factorization:
| 103 | 103 |
| 1 |
Prime factors of 103 are 103.
103 = 1031
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: 3,11,103
.32×111×1031 = 10197
This shows that the LCM of 99 and 103 is 10197.
How to Calculate the LCM of 99 and 103 Using Common Multiples
The first step in determining the Least Common Multiple of 99 and 103 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 99 and 103:
Lets look at the first ten multiples of these numbers, 99 and 103:
99,198,297,396,495,594,693,792,891,1683 are the first ten multiples of 99.
103,206,309,412,515,618,721,824,927,1751 are the first ten multiples of 103.
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 99 and 103, for example, are 1188, 1683, and 1648. 10197 is the least common multiple since it is the smallest.
99 and 103 have an LCM of 10197.
Least Common Multiple of 99 and 103 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 99 and 103, than apply into the LCM equation.
GCF(99,103) = 1
LCM(99,103) = ( 99 × 103) / 1
LCM(99,103) = 10197 / 1
LCM(99,103) = 10197
Related Least Common Multiples of 99
Related Least Common Multiples of 103
Frequently Asked Questions on LCM of 99 and 103
1. What is the LCM of 99 and 103?
The LCM of 99 and 103 is 10197.
2. How to find the lowest common multiple of 99 and 103?
To find the lowest common multiple of 99 and 103, we have to get the multip;es of both numbers and identify the least common multiple in them which is 10197.
3. What are the Factors of 99?
Answer: Factors of 99 are 1, 3, 9, 11, 33, 99. There are 6 integers that are factors of 99. The greatest factor of 99 is 99.
4. 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.
5. How to Find the LCM of 99 and 103?Answer:
Least Common Multiple of 99 and 103 = 10197
Step 1: Find the prime factorization of 99
99 = 3 x 3 x 11
Step 2: Find the prime factorization of 103
103 = 103
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 10197 = 3 x 3 x 11 x 103
Step 4: Therefore, the least common multiple of 99 and 103 is 10197.