LCM of 135 and 142
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 135 and 142 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 19170 as output. Here you can check the answer for Find the LCM of 135 and 142.
What is LCM of 135 and 142
Given Numbers are 135, 142
We can find the LCM of 135, 142 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 135 and 142
Multiples of 135 =135,270,405,540,675,810,945,1080,1215,1350,1485,1620,1755,1890,2025,2160,2295,
Multiples of 142 =142,284,426,568,710,852,994,1136,1278,1420,1562,1704,1846,1988,2130,2272,2414,
Now, get the least common multiple of 135, 142 which is 19170
So, the LCM of 135, 142 is 19170.
Least Common Multiple (LCM) of 135 and 142 with the help of Prime Factorisation
One method for determining the LCM of 135 and 142 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 142's prime factorization:
| 2 | 142 |
| 71 | 71 |
| 1 |
Prime factors of 142 are 2,71.
142 = 21×711
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, 2,71
.21×33×51×711 = 19170
This shows that the LCM of 135 and 142 is 19170.
How to Calculate the LCM of 135 and 142 Using Common Multiples
The first step in determining the Least Common Multiple of 135 and 142 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 135 and 142:
Lets look at the first ten multiples of these numbers, 135 and 142:
135,270,405,540,675,810,945,1080,1215,2295 are the first ten multiples of 135.
142,284,426,568,710,852,994,1136,1278,2414 are the first ten multiples of 142.
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 142, for example, are 1620, 2295, and 2272. 19170 is the least common multiple since it is the smallest.
135 and 142 have an LCM of 19170.
Least Common Multiple of 135 and 142 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 142, than apply into the LCM equation.
GCF(135,142) = 1
LCM(135,142) = ( 135 × 142) / 1
LCM(135,142) = 19170 / 1
LCM(135,142) = 19170
Related Least Common Multiples of 135
Related Least Common Multiples of 142
Frequently Asked Questions on LCM of 135 and 142
1. What is the LCM of 135 and 142?
The LCM of 135 and 142 is 19170.
2. How to find the lowest common multiple of 135 and 142?
To find the lowest common multiple of 135 and 142, we have to get the multip;es of both numbers and identify the least common multiple in them which is 19170.
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 142?
Answer: Factors of 142 are 1, 2, 71, 142. There are 4 integers that are factors of 142. The greatest factor of 142 is 142.
5. How to Find the LCM of 135 and 142?Answer:
Least Common Multiple of 135 and 142 = 19170
Step 1: Find the prime factorization of 135
135 = 3 x 3 x 3 x 5
Step 2: Find the prime factorization of 142
142 = 2 x 71
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 19170 = 2 x 3 x 3 x 3 x 5 x 71
Step 4: Therefore, the least common multiple of 135 and 142 is 19170.