LCM of 130 and 135
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 130 and 135 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 3510 as output. Here you can check the answer for Find the LCM of 130 and 135.
What is LCM of 130 and 135
Given Numbers are 130, 135
We can find the LCM of 130, 135 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 130 and 135
Multiples of 130 =130,260,390,520,650,780,910,1040,1170,1300,1430,1560,1690,1820,1950,2080,2210,
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 130, 135 which is 3510
So, the LCM of 130, 135 is 3510.
Least Common Multiple (LCM) of 130 and 135 with the help of Prime Factorisation
One method for determining the LCM of 130 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 130's prime factorization:
| 2 | 130 |
| 5 | 65 |
| 13 | 13 |
| 1 |
Prime factors of 130 are 2, 5,13.
130 = 21×51×131
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, 5,13,3
.21×33×51×131 = 3510
This shows that the LCM of 130 and 135 is 3510.
How to Calculate the LCM of 130 and 135 Using Common Multiples
The first step in determining the Least Common Multiple of 130 and 135 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 130 and 135:
Lets look at the first ten multiples of these numbers, 130 and 135:
130,260,390,520,650,780,910,1040,1170,2210 are the first ten multiples of 130.
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 130 and 135, for example, are 1560, 2210, and 2160. 3510 is the least common multiple since it is the smallest.
130 and 135 have an LCM of 3510.
Least Common Multiple of 130 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 130 and 135, than apply into the LCM equation.
GCF(130,135) = 5
LCM(130,135) = ( 130 × 135) / 5
LCM(130,135) = 17550 / 5
LCM(130,135) = 3510
Related Least Common Multiples of 130
Related Least Common Multiples of 135
Frequently Asked Questions on LCM of 130 and 135
1. What is the LCM of 130 and 135?
The LCM of 130 and 135 is 3510.
2. How to find the lowest common multiple of 130 and 135?
To find the lowest common multiple of 130 and 135, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3510.
3. What are the Factors of 130?
Answer: Factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130. There are 8 integers that are factors of 130. The greatest factor of 130 is 130.
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 130 and 135?Answer:
Least Common Multiple of 130 and 135 = 3510
Step 1: Find the prime factorization of 130
130 = 2 x 5 x 13
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 = 3510 = 2 x 3 x 3 x 3 x 5 x 13
Step 4: Therefore, the least common multiple of 130 and 135 is 3510.