LCM of 135 and 141
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 135 and 141 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 6345 as output. Here you can check the answer for Find the LCM of 135 and 141.
What is LCM of 135 and 141
Given Numbers are 135, 141
We can find the LCM of 135, 141 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 135 and 141
Multiples of 135 =135,270,405,540,675,810,945,1080,1215,1350,1485,1620,1755,1890,2025,2160,2295,
Multiples of 141 =141,282,423,564,705,846,987,1128,1269,1410,1551,1692,1833,1974,2115,2256,2397,
Now, get the least common multiple of 135, 141 which is 6345
So, the LCM of 135, 141 is 6345.
Least Common Multiple (LCM) of 135 and 141 with the help of Prime Factorisation
One method for determining the LCM of 135 and 141 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 135's prime factorization:
| 3 | 135 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 135 are 3,5.
135 = 33×51
And this is 141's prime factorization:
| 3 | 141 |
| 47 | 47 |
| 1 |
Prime factors of 141 are 3,47.
141 = 31×471
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: 3,5,47
.33×51×471 = 6345
This shows that the LCM of 135 and 141 is 6345.
How to Calculate the LCM of 135 and 141 Using Common Multiples
The first step in determining the Least Common Multiple of 135 and 141 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 135 and 141:
Lets look at the first ten multiples of these numbers, 135 and 141:
135,270,405,540,675,810,945,1080,1215,2295 are the first ten multiples of 135.
141,282,423,564,705,846,987,1128,1269,2397 are the first ten multiples of 141.
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 135 and 141, for example, are 1620, 2295, and 2256. 6345 is the least common multiple since it is the smallest.
135 and 141 have an LCM of 6345.
Least Common Multiple of 135 and 141 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 135 and 141, than apply into the LCM equation.
GCF(135,141) = 3
LCM(135,141) = ( 135 × 141) / 3
LCM(135,141) = 19035 / 3
LCM(135,141) = 6345
Related Least Common Multiples of 135
Related Least Common Multiples of 141
Frequently Asked Questions on LCM of 135 and 141
1. What is the LCM of 135 and 141?
The LCM of 135 and 141 is 6345.
2. How to find the lowest common multiple of 135 and 141?
To find the lowest common multiple of 135 and 141, we have to get the multip;es of both numbers and identify the least common multiple in them which is 6345.
3. 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.
4. What are the Factors of 141?
Answer: Factors of 141 are 1, 3, 47, 141. There are 4 integers that are factors of 141. The greatest factor of 141 is 141.
5. How to Find the LCM of 135 and 141?Answer:
Least Common Multiple of 135 and 141 = 6345
Step 1: Find the prime factorization of 135
135 = 3 x 3 x 3 x 5
Step 2: Find the prime factorization of 141
141 = 3 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6345 = 3 x 3 x 3 x 5 x 47
Step 4: Therefore, the least common multiple of 135 and 141 is 6345.