LCM of 123 and 129
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 123 and 129 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 5289 as output. Here you can check the answer for Find the LCM of 123 and 129.
What is LCM of 123 and 129
Given Numbers are 123, 129
We can find the LCM of 123, 129 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 123 and 129
Multiples of 123 =123,246,369,492,615,738,861,984,1107,1230,1353,1476,1599,1722,1845,1968,2091,
Multiples of 129 =129,258,387,516,645,774,903,1032,1161,1290,1419,1548,1677,1806,1935,2064,2193,
Now, get the least common multiple of 123, 129 which is 5289
So, the LCM of 123, 129 is 5289.
Least Common Multiple (LCM) of 123 and 129 with the help of Prime Factorisation
One method for determining the LCM of 123 and 129 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 123's prime factorization:
| 3 | 123 |
| 41 | 41 |
| 1 |
Prime factors of 123 are 3,41.
123 = 31×411
And this is 129's prime factorization:
| 3 | 129 |
| 43 | 43 |
| 1 |
Prime factors of 129 are 3,43.
129 = 31×431
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: 3,41,43
.31×411×431 = 5289
This shows that the LCM of 123 and 129 is 5289.
How to Calculate the LCM of 123 and 129 Using Common Multiples
The first step in determining the Least Common Multiple of 123 and 129 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 123 and 129:
Lets look at the first ten multiples of these numbers, 123 and 129:
123,246,369,492,615,738,861,984,1107,2091 are the first ten multiples of 123.
129,258,387,516,645,774,903,1032,1161,2193 are the first ten multiples of 129.
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 123 and 129, for example, are 1476, 2091, and 2064. 5289 is the least common multiple since it is the smallest.
123 and 129 have an LCM of 5289.
Least Common Multiple of 123 and 129 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 123 and 129, than apply into the LCM equation.
GCF(123,129) = 3
LCM(123,129) = ( 123 × 129) / 3
LCM(123,129) = 15867 / 3
LCM(123,129) = 5289
Related Least Common Multiples of 123
Related Least Common Multiples of 129
Frequently Asked Questions on LCM of 123 and 129
1. What is the LCM of 123 and 129?
The LCM of 123 and 129 is 5289.
2. How to find the lowest common multiple of 123 and 129?
To find the lowest common multiple of 123 and 129, we have to get the multip;es of both numbers and identify the least common multiple in them which is 5289.
3. 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.
4. What are the Factors of 129?
Answer: Factors of 129 are 1, 3, 43, 129. There are 4 integers that are factors of 129. The greatest factor of 129 is 129.
5. How to Find the LCM of 123 and 129?Answer:
Least Common Multiple of 123 and 129 = 5289
Step 1: Find the prime factorization of 123
123 = 3 x 41
Step 2: Find the prime factorization of 129
129 = 3 x 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5289 = 3 x 41 x 43
Step 4: Therefore, the least common multiple of 123 and 129 is 5289.