Least Common Multiple of 231 and 238
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 231 and 238 the smallest integer that is 7854 that is divisible by both numbers.
Least Common Multiple (LCM) of 231 and 238 is 7854.
LCM(231,238) = 7854
LCM of 231 and 238
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 231 and 238 by Prime method
- Least Common Multiple of 231 and 238 with GCF Formula
LCM of 231 and 238 is 7854
Least common multiple can be found by multiplying the highest exponent prime factors of 231 and 238. First we will calculate the prime factors of 231 and 238.
Prime Factorization of 231
| 3 | 231 |
| 7 | 77 |
| 11 | 11 |
| 1 |
Prime factors of 231 are 3, 7,11. Prime factorization of 231 in exponential form is:
231 = 31×71×111
Prime Factorization of 238
| 2 | 238 |
| 7 | 119 |
| 17 | 17 |
| 1 |
Prime factors of 238 are 2, 7,17. Prime factorization of 238 in exponential form is:
238 = 21×71×171
Now multiplying the highest exponent prime factors to calculate the LCM of 231 and 238.
LCM(231,238) = 21×31×71×111×171
LCM(231,238) = 7854
Factors of 231
List of positive integer factors of 231 that divides 231 without a remainder.
1, 3, 7, 11, 21, 33, 77, 231
Factors of 238
List of positive integer factors of 238 that divides 238 without a remainder.
1, 2, 7, 14, 17, 34, 119, 238
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
Properties of LCM 231 and 238
(i) The LCM of 238 and 231 is associative
LCM of 231 and 238 = LCM of 238 and 231
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?
Answer: LCM of 231 and 238 is 7854.
2. 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.
3. 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.
4. 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.