LCM of 128 and 135
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 128 and 135 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 17280 as output. Here you can check the answer for Find the LCM of 128 and 135.
What is LCM of 128 and 135
Given Numbers are 128, 135
We can find the LCM of 128, 135 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 128 and 135
Multiples of 128 =128,256,384,512,640,768,896,1024,1152,1280,1408,1536,1664,1792,1920,2048,2176,
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 128, 135 which is 17280
So, the LCM of 128, 135 is 17280.
Least Common Multiple (LCM) of 128 and 135 with the help of Prime Factorisation
One method for determining the LCM of 128 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 128's prime factorization:
| 2 | 128 |
| 2 | 64 |
| 2 | 32 |
| 2 | 16 |
| 2 | 8 |
| 2 | 4 |
| 2 | 2 |
| 1 |
Prime factors of 128 are 2.
128 = 27
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:2, 3,5
.27×33×51 = 17280
This shows that the LCM of 128 and 135 is 17280.
How to Calculate the LCM of 128 and 135 Using Common Multiples
The first step in determining the Least Common Multiple of 128 and 135 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 128 and 135:
Lets look at the first ten multiples of these numbers, 128 and 135:
128,256,384,512,640,768,896,1024,1152,2176 are the first ten multiples of 128.
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 128 and 135, for example, are 1536, 2176, and 2160. 17280 is the least common multiple since it is the smallest.
128 and 135 have an LCM of 17280.
Least Common Multiple of 128 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 128 and 135, than apply into the LCM equation.
GCF(128,135) = 1
LCM(128,135) = ( 128 × 135) / 1
LCM(128,135) = 17280 / 1
LCM(128,135) = 17280
Related Least Common Multiples of 128
Related Least Common Multiples of 135
Frequently Asked Questions on LCM of 128 and 135
1. What is the LCM of 128 and 135?
The LCM of 128 and 135 is 17280.
2. How to find the lowest common multiple of 128 and 135?
To find the lowest common multiple of 128 and 135, we have to get the multip;es of both numbers and identify the least common multiple in them which is 17280.
3. What are the Factors of 128?
Answer: Factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128. There are 8 integers that are factors of 128. The greatest factor of 128 is 128.
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 128 and 135?Answer:
Least Common Multiple of 128 and 135 = 17280
Step 1: Find the prime factorization of 128
128 = 2 x 2 x 2 x 2 x 2 x 2 x 2
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 = 17280 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 128 and 135 is 17280.