Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 17231 and 17238 the smallest integer that is 297027978 that is divisible by both numbers.
Least Common Multiple (LCM) of 17231 and 17238 is 297027978.
LCM(17231,17238) = 297027978
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 17231 and 17238. First we will calculate the prime factors of 17231 and 17238.
Prime Factorization of 17231
17231 | 17231 |
1 |
Prime factors of 17231 are 17231. Prime factorization of 17231 in exponential form is:
17231 = 172311
Prime Factorization of 17238
2 | 17238 |
3 | 8619 |
13 | 2873 |
13 | 221 |
17 | 17 |
1 |
Prime factors of 17238 are 2, 3, 13,17. Prime factorization of 17238 in exponential form is:
17238 = 21×31×132×171
Now multiplying the highest exponent prime factors to calculate the LCM of 17231 and 17238.
LCM(17231,17238) = 21×31×132×171×172311
LCM(17231,17238) = 297027978
Factors of 17231
List of positive integer factors of 17231 that divides 17231 without a remainder.
1, 17231
Factors of 17238
List of positive integer factors of 17238 that divides 17238 without a remainder.
1, 2, 3, 6, 13, 17, 26, 34, 39, 51, 78, 102, 169, 221, 338, 442, 507, 663, 1014, 1326, 2873, 5746, 8619, 17238
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17231 and 17238, than apply into the LCM equation.
GCF(17231,17238) = 1
LCM(17231,17238) = ( 17231 × 17238) / 1
LCM(17231,17238) = 297027978 / 1
LCM(17231,17238) = 297027978
(i) The LCM of 17238 and 17231 is associative
LCM of 17231 and 17238 = LCM of 17238 and 17231
1. What is the LCM of 17231 and 17238?
Answer: LCM of 17231 and 17238 is 297027978.
2. What are the Factors of 17231?
Answer: Factors of 17231 are 1, 17231. There are 2 integers that are factors of 17231. The greatest factor of 17231 is 17231.
3. What are the Factors of 17238?
Answer: Factors of 17238 are 1, 2, 3, 6, 13, 17, 26, 34, 39, 51, 78, 102, 169, 221, 338, 442, 507, 663, 1014, 1326, 2873, 5746, 8619, 17238. There are 24 integers that are factors of 17238. The greatest factor of 17238 is 17238.
4. How to Find the LCM of 17231 and 17238?
Answer:
Least Common Multiple of 17231 and 17238 = 297027978
Step 1: Find the prime factorization of 17231
17231 = 17231
Step 2: Find the prime factorization of 17238
17238 = 2 x 3 x 13 x 13 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 = 297027978 = 2 x 3 x 13 x 13 x 17 x 17231
Step 4: Therefore, the least common multiple of 17231 and 17238 is 297027978.