LCM of 270 and 276
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 270 and 276 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 12420 as output. Here you can check the answer for Find the LCM of 270 and 276.
What is LCM of 270 and 276
Given Numbers are 270, 276
We can find the LCM of 270, 276 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 270 and 276
Multiples of 270 =270,540,810,1080,1350,1620,1890,2160,2430,2700,2970,3240,3510,3780,4050,4320,4590,
Multiples of 276 =276,552,828,1104,1380,1656,1932,2208,2484,2760,3036,3312,3588,3864,4140,4416,4692,
Now, get the least common multiple of 270, 276 which is 12420
So, the LCM of 270, 276 is 12420.
Least Common Multiple (LCM) of 270 and 276 with the help of Prime Factorisation
One method for determining the LCM of 270 and 276 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 276's prime factorization:
| 2 | 276 |
| 2 | 138 |
| 3 | 69 |
| 23 | 23 |
| 1 |
Prime factors of 276 are 2, 3,23.
276 = 22×31×231
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, 3,5,23
.22×33×51×231 = 12420
This shows that the LCM of 270 and 276 is 12420.
How to Calculate the LCM of 270 and 276 Using Common Multiples
The first step in determining the Least Common Multiple of 270 and 276 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 270 and 276:
Lets look at the first ten multiples of these numbers, 270 and 276:
270,540,810,1080,1350,1620,1890,2160,2430,4590 are the first ten multiples of 270.
276,552,828,1104,1380,1656,1932,2208,2484,4692 are the first ten multiples of 276.
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 276, for example, are 3240, 4590, and 4416. 12420 is the least common multiple since it is the smallest.
270 and 276 have an LCM of 12420.
Least Common Multiple of 270 and 276 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 276, than apply into the LCM equation.
GCF(270,276) = 6
LCM(270,276) = ( 270 × 276) / 6
LCM(270,276) = 74520 / 6
LCM(270,276) = 12420
Related Least Common Multiples of 270
Related Least Common Multiples of 276
Frequently Asked Questions on LCM of 270 and 276
1. What is the LCM of 270 and 276?
The LCM of 270 and 276 is 12420.
2. How to find the lowest common multiple of 270 and 276?
To find the lowest common multiple of 270 and 276, we have to get the multip;es of both numbers and identify the least common multiple in them which is 12420.
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 276?
Answer: Factors of 276 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276. There are 12 integers that are factors of 276. The greatest factor of 276 is 276.
5. How to Find the LCM of 270 and 276?Answer:
Least Common Multiple of 270 and 276 = 12420
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 276
276 = 2 x 2 x 3 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 12420 = 2 x 2 x 3 x 3 x 3 x 5 x 23
Step 4: Therefore, the least common multiple of 270 and 276 is 12420.