Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 17232 and 17238 the smallest integer that is 49507536 that is divisible by both numbers.
Least Common Multiple (LCM) of 17232 and 17238 is 49507536.
LCM(17232,17238) = 49507536
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 17232 and 17238. First we will calculate the prime factors of 17232 and 17238.
Prime Factorization of 17232
2 | 17232 |
2 | 8616 |
2 | 4308 |
2 | 2154 |
3 | 1077 |
359 | 359 |
1 |
Prime factors of 17232 are 2, 3,359. Prime factorization of 17232 in exponential form is:
17232 = 24×31×3591
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 17232 and 17238.
LCM(17232,17238) = 24×31×132×171×3591
LCM(17232,17238) = 49507536
Factors of 17232
List of positive integer factors of 17232 that divides 17232 without a remainder.
1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 359, 718, 1077, 1436, 2154, 2872, 4308, 5744, 8616, 17232
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 17232 and 17238, than apply into the LCM equation.
GCF(17232,17238) = 6
LCM(17232,17238) = ( 17232 × 17238) / 6
LCM(17232,17238) = 297045216 / 6
LCM(17232,17238) = 49507536
(i) The LCM of 17238 and 17232 is associative
LCM of 17232 and 17238 = LCM of 17238 and 17232
1. What is the LCM of 17232 and 17238?
Answer: LCM of 17232 and 17238 is 49507536.
2. What are the Factors of 17232?
Answer: Factors of 17232 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 359, 718, 1077, 1436, 2154, 2872, 4308, 5744, 8616, 17232. There are 20 integers that are factors of 17232. The greatest factor of 17232 is 17232.
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 17232 and 17238?
Answer:
Least Common Multiple of 17232 and 17238 = 49507536
Step 1: Find the prime factorization of 17232
17232 = 2 x 2 x 2 x 2 x 3 x 359
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 = 49507536 = 2 x 2 x 2 x 2 x 3 x 13 x 13 x 17 x 359
Step 4: Therefore, the least common multiple of 17232 and 17238 is 49507536.