LCM of 117 and 123
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 117 and 123 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 4797 as output. Here you can check the answer for Find the LCM of 117 and 123.
What is LCM of 117 and 123
Given Numbers are 117, 123
We can find the LCM of 117, 123 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 117 and 123
Multiples of 117 =117,234,351,468,585,702,819,936,1053,1170,1287,1404,1521,1638,1755,1872,1989,
Multiples of 123 =123,246,369,492,615,738,861,984,1107,1230,1353,1476,1599,1722,1845,1968,2091,
Now, get the least common multiple of 117, 123 which is 4797
So, the LCM of 117, 123 is 4797.
Least Common Multiple (LCM) of 117 and 123 with the help of Prime Factorisation
One method for determining the LCM of 117 and 123 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 117's prime factorization:
| 3 | 117 |
| 3 | 39 |
| 13 | 13 |
| 1 |
Prime factors of 117 are 3,13.
117 = 32×131
And this is 123's prime factorization:
| 3 | 123 |
| 41 | 41 |
| 1 |
Prime factors of 123 are 3,41.
123 = 31×411
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: 3,13,41
.32×131×411 = 4797
This shows that the LCM of 117 and 123 is 4797.
How to Calculate the LCM of 117 and 123 Using Common Multiples
The first step in determining the Least Common Multiple of 117 and 123 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 117 and 123:
Lets look at the first ten multiples of these numbers, 117 and 123:
117,234,351,468,585,702,819,936,1053,1989 are the first ten multiples of 117.
123,246,369,492,615,738,861,984,1107,2091 are the first ten multiples of 123.
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 117 and 123, for example, are 1404, 1989, and 1968. 4797 is the least common multiple since it is the smallest.
117 and 123 have an LCM of 4797.
Least Common Multiple of 117 and 123 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 117 and 123, than apply into the LCM equation.
GCF(117,123) = 3
LCM(117,123) = ( 117 × 123) / 3
LCM(117,123) = 14391 / 3
LCM(117,123) = 4797
Related Least Common Multiples of 117
Related Least Common Multiples of 123
Frequently Asked Questions on LCM of 117 and 123
1. What is the LCM of 117 and 123?
The LCM of 117 and 123 is 4797.
2. How to find the lowest common multiple of 117 and 123?
To find the lowest common multiple of 117 and 123, we have to get the multip;es of both numbers and identify the least common multiple in them which is 4797.
3. What are the Factors of 117?
Answer: Factors of 117 are 1, 3, 9, 13, 39, 117. There are 6 integers that are factors of 117. The greatest factor of 117 is 117.
4. What are the Factors of 123?
Answer: Factors of 123 are 1, 3, 41, 123. There are 4 integers that are factors of 123. The greatest factor of 123 is 123.
5. How to Find the LCM of 117 and 123?Answer:
Least Common Multiple of 117 and 123 = 4797
Step 1: Find the prime factorization of 117
117 = 3 x 3 x 13
Step 2: Find the prime factorization of 123
123 = 3 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4797 = 3 x 3 x 13 x 41
Step 4: Therefore, the least common multiple of 117 and 123 is 4797.