LCM of 129 and 135
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 129 and 135 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 5805 as output. Here you can check the answer for Find the LCM of 129 and 135.
What is LCM of 129 and 135
Given Numbers are 129, 135
We can find the LCM of 129, 135 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 129 and 135
Multiples of 129 =129,258,387,516,645,774,903,1032,1161,1290,1419,1548,1677,1806,1935,2064,2193,
Multiples of 135 =135,270,405,540,675,810,945,1080,1215,1350,1485,1620,1755,1890,2025,2160,2295,
Now, get the least common multiple of 129, 135 which is 5805
So, the LCM of 129, 135 is 5805.
Least Common Multiple (LCM) of 129 and 135 with the help of Prime Factorisation
One method for determining the LCM of 129 and 135 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 129's prime factorization:
| 3 | 129 |
| 43 | 43 |
| 1 |
Prime factors of 129 are 3,43.
129 = 31×431
And this is 135's prime factorization:
| 3 | 135 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 135 are 3,5.
135 = 33×51
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: 3,43,5
.33×51×431 = 5805
This shows that the LCM of 129 and 135 is 5805.
How to Calculate the LCM of 129 and 135 Using Common Multiples
The first step in determining the Least Common Multiple of 129 and 135 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 129 and 135:
Lets look at the first ten multiples of these numbers, 129 and 135:
129,258,387,516,645,774,903,1032,1161,2193 are the first ten multiples of 129.
135,270,405,540,675,810,945,1080,1215,2295 are the first ten multiples of 135.
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 129 and 135, for example, are 1548, 2193, and 2160. 5805 is the least common multiple since it is the smallest.
129 and 135 have an LCM of 5805.
Least Common Multiple of 129 and 135 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 129 and 135, than apply into the LCM equation.
GCF(129,135) = 3
LCM(129,135) = ( 129 × 135) / 3
LCM(129,135) = 17415 / 3
LCM(129,135) = 5805
Related Least Common Multiples of 129
Related Least Common Multiples of 135
Frequently Asked Questions on LCM of 129 and 135
1. What is the LCM of 129 and 135?
The LCM of 129 and 135 is 5805.
2. How to find the lowest common multiple of 129 and 135?
To find the lowest common multiple of 129 and 135, we have to get the multip;es of both numbers and identify the least common multiple in them which is 5805.
3. 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.
4. What are the Factors of 135?
Answer: Factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135. There are 8 integers that are factors of 135. The greatest factor of 135 is 135.
5. How to Find the LCM of 129 and 135?Answer:
Least Common Multiple of 129 and 135 = 5805
Step 1: Find the prime factorization of 129
129 = 3 x 43
Step 2: Find the prime factorization of 135
135 = 3 x 3 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 5805 = 3 x 3 x 3 x 5 x 43
Step 4: Therefore, the least common multiple of 129 and 135 is 5805.