LCM of 270 and 278
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 270 and 278 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 37530 as output. Here you can check the answer for Find the LCM of 270 and 278.
What is LCM of 270 and 278
Given Numbers are 270, 278
We can find the LCM of 270, 278 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 270 and 278
Multiples of 270 =270,540,810,1080,1350,1620,1890,2160,2430,2700,2970,3240,3510,3780,4050,4320,4590,
Multiples of 278 =278,556,834,1112,1390,1668,1946,2224,2502,2780,3058,3336,3614,3892,4170,4448,4726,
Now, get the least common multiple of 270, 278 which is 37530
So, the LCM of 270, 278 is 37530.
Least Common Multiple (LCM) of 270 and 278 with the help of Prime Factorisation
One method for determining the LCM of 270 and 278 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 270's prime factorization:
| 2 | 270 |
| 3 | 135 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 270 are 2, 3,5.
270 = 21×33×51
And this is 278's prime factorization:
| 2 | 278 |
| 139 | 139 |
| 1 |
Prime factors of 278 are 2,139.
278 = 21×1391
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, 3,5,139
.21×33×51×1391 = 37530
This shows that the LCM of 270 and 278 is 37530.
How to Calculate the LCM of 270 and 278 Using Common Multiples
The first step in determining the Least Common Multiple of 270 and 278 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 270 and 278:
Lets look at the first ten multiples of these numbers, 270 and 278:
270,540,810,1080,1350,1620,1890,2160,2430,4590 are the first ten multiples of 270.
278,556,834,1112,1390,1668,1946,2224,2502,4726 are the first ten multiples of 278.
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 270 and 278, for example, are 3240, 4590, and 4448. 37530 is the least common multiple since it is the smallest.
270 and 278 have an LCM of 37530.
Least Common Multiple of 270 and 278 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 270 and 278, than apply into the LCM equation.
GCF(270,278) = 2
LCM(270,278) = ( 270 × 278) / 2
LCM(270,278) = 75060 / 2
LCM(270,278) = 37530
Related Least Common Multiples of 270
Related Least Common Multiples of 278
Frequently Asked Questions on LCM of 270 and 278
1. What is the LCM of 270 and 278?
The LCM of 270 and 278 is 37530.
2. How to find the lowest common multiple of 270 and 278?
To find the lowest common multiple of 270 and 278, we have to get the multip;es of both numbers and identify the least common multiple in them which is 37530.
3. What are the Factors of 270?
Answer: Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270. There are 16 integers that are factors of 270. The greatest factor of 270 is 270.
4. What are the Factors of 278?
Answer: Factors of 278 are 1, 2, 139, 278. There are 4 integers that are factors of 278. The greatest factor of 278 is 278.
5. How to Find the LCM of 270 and 278?Answer:
Least Common Multiple of 270 and 278 = 37530
Step 1: Find the prime factorization of 270
270 = 2 x 3 x 3 x 3 x 5
Step 2: Find the prime factorization of 278
278 = 2 x 139
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 37530 = 2 x 3 x 3 x 3 x 5 x 139
Step 4: Therefore, the least common multiple of 270 and 278 is 37530.