LCM of 135 and 140
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 135 and 140 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 3780 as output. Here you can check the answer for Find the LCM of 135 and 140.
What is LCM of 135 and 140
Given Numbers are 135, 140
We can find the LCM of 135, 140 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 135 and 140
Multiples of 135 =135,270,405,540,675,810,945,1080,1215,1350,1485,1620,1755,1890,2025,2160,2295,
Multiples of 140 =140,280,420,560,700,840,980,1120,1260,1400,1540,1680,1820,1960,2100,2240,2380,
Now, get the least common multiple of 135, 140 which is 3780
So, the LCM of 135, 140 is 3780.
Least Common Multiple (LCM) of 135 and 140 with the help of Prime Factorisation
One method for determining the LCM of 135 and 140 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 140's prime factorization:
| 2 | 140 |
| 2 | 70 |
| 5 | 35 |
| 7 | 7 |
| 1 |
Prime factors of 140 are 2, 5,7.
140 = 22×51×71
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, 2,7
.22×33×51×71 = 3780
This shows that the LCM of 135 and 140 is 3780.
How to Calculate the LCM of 135 and 140 Using Common Multiples
The first step in determining the Least Common Multiple of 135 and 140 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 135 and 140:
Lets look at the first ten multiples of these numbers, 135 and 140:
135,270,405,540,675,810,945,1080,1215,2295 are the first ten multiples of 135.
140,280,420,560,700,840,980,1120,1260,2380 are the first ten multiples of 140.
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 140, for example, are 1620, 2295, and 2240. 3780 is the least common multiple since it is the smallest.
135 and 140 have an LCM of 3780.
Least Common Multiple of 135 and 140 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 140, than apply into the LCM equation.
GCF(135,140) = 5
LCM(135,140) = ( 135 × 140) / 5
LCM(135,140) = 18900 / 5
LCM(135,140) = 3780
Related Least Common Multiples of 135
Related Least Common Multiples of 140
Frequently Asked Questions on LCM of 135 and 140
1. What is the LCM of 135 and 140?
The LCM of 135 and 140 is 3780.
2. How to find the lowest common multiple of 135 and 140?
To find the lowest common multiple of 135 and 140, we have to get the multip;es of both numbers and identify the least common multiple in them which is 3780.
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 140?
Answer: Factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140. There are 12 integers that are factors of 140. The greatest factor of 140 is 140.
5. How to Find the LCM of 135 and 140?Answer:
Least Common Multiple of 135 and 140 = 3780
Step 1: Find the prime factorization of 135
135 = 3 x 3 x 3 x 5
Step 2: Find the prime factorization of 140
140 = 2 x 2 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3780 = 2 x 2 x 3 x 3 x 3 x 5 x 7
Step 4: Therefore, the least common multiple of 135 and 140 is 3780.