LCM of 231 and 238
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
It is easy to find the LCM of 231 and 238 with the help of the handy LCM Calculator. You have to enter 44, and 60 as inputs to avail the LCM 7854 as output. Here you can check the answer for Find the LCM of 231 and 238.
What is LCM of 231 and 238
Given Numbers are 231, 238
We can find the LCM of 231, 238 using the brute force method, prime factorization method, or GCD method.
To use brute force method, list the multiples of 231 and 238
Multiples of 231 =231,462,693,924,1155,1386,1617,1848,2079,2310,2541,2772,3003,3234,3465,3696,3927,
Multiples of 238 =238,476,714,952,1190,1428,1666,1904,2142,2380,2618,2856,3094,3332,3570,3808,4046,
Now, get the least common multiple of 231, 238 which is 7854
So, the LCM of 231, 238 is 7854.
Least Common Multiple (LCM) of 231 and 238 with the help of Prime Factorisation
One method for determining the LCM of 231 and 238 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 231's prime factorization:
| 3 | 231 |
| 7 | 77 |
| 11 | 11 |
| 1 |
Prime factors of 231 are 3, 7,11.
231 = 31×71×111
And this is 238's prime factorization:
| 2 | 238 |
| 7 | 119 |
| 17 | 17 |
| 1 |
Prime factors of 238 are 2, 7,17.
238 = 21×71×171
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, 7,11, 2,17
.21×31×71×111×171 = 7854
This shows that the LCM of 231 and 238 is 7854.
How to Calculate the LCM of 231 and 238 Using Common Multiples
The first step in determining the Least Common Multiple of 231 and 238 is to generate a list of multiples for each number.
Lets look at the multiples of these two numbers, 231 and 238:
Lets look at the first ten multiples of these numbers, 231 and 238:
231,462,693,924,1155,1386,1617,1848,2079,3927 are the first ten multiples of 231.
238,476,714,952,1190,1428,1666,1904,2142,4046 are the first ten multiples of 238.
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 231 and 238, for example, are 2772, 3927, and 3808. 7854 is the least common multiple since it is the smallest.
231 and 238 have an LCM of 7854.
Least Common Multiple of 231 and 238 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 231 and 238, than apply into the LCM equation.
GCF(231,238) = 7
LCM(231,238) = ( 231 × 238) / 7
LCM(231,238) = 54978 / 7
LCM(231,238) = 7854
Related Least Common Multiples of 231
Related Least Common Multiples of 238
Frequently Asked Questions on LCM of 231 and 238
1. What is the LCM of 231 and 238?
The LCM of 231 and 238 is 7854.
2. How to find the lowest common multiple of 231 and 238?
To find the lowest common multiple of 231 and 238, we have to get the multip;es of both numbers and identify the least common multiple in them which is 7854.
3. What are the Factors of 231?
Answer: Factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231. There are 8 integers that are factors of 231. The greatest factor of 231 is 231.
4. What are the Factors of 238?
Answer: Factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238. There are 8 integers that are factors of 238. The greatest factor of 238 is 238.
5. How to Find the LCM of 231 and 238?Answer:
Least Common Multiple of 231 and 238 = 7854
Step 1: Find the prime factorization of 231
231 = 3 x 7 x 11
Step 2: Find the prime factorization of 238
238 = 2 x 7 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7854 = 2 x 3 x 7 x 11 x 17
Step 4: Therefore, the least common multiple of 231 and 238 is 7854.