Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2509 and 2517 the smallest integer that is 6315153 that is divisible by both numbers.
Least Common Multiple (LCM) of 2509 and 2517 is 6315153.
LCM(2509,2517) = 6315153
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 2509 and 2517. First we will calculate the prime factors of 2509 and 2517.
Prime Factorization of 2509
13 | 2509 |
193 | 193 |
1 |
Prime factors of 2509 are 13,193. Prime factorization of 2509 in exponential form is:
2509 = 131×1931
Prime Factorization of 2517
3 | 2517 |
839 | 839 |
1 |
Prime factors of 2517 are 3,839. Prime factorization of 2517 in exponential form is:
2517 = 31×8391
Now multiplying the highest exponent prime factors to calculate the LCM of 2509 and 2517.
LCM(2509,2517) = 31×131×1931×8391
LCM(2509,2517) = 6315153
Factors of 2509
List of positive integer factors of 2509 that divides 2509 without a remainder.
1, 13, 193, 2509
Factors of 2517
List of positive integer factors of 2517 that divides 2517 without a remainder.
1, 3, 839, 2517
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2509 and 2517, than apply into the LCM equation.
GCF(2509,2517) = 1
LCM(2509,2517) = ( 2509 × 2517) / 1
LCM(2509,2517) = 6315153 / 1
LCM(2509,2517) = 6315153
(i) The LCM of 2517 and 2509 is associative
LCM of 2509 and 2517 = LCM of 2517 and 2509
1. What is the LCM of 2509 and 2517?
Answer: LCM of 2509 and 2517 is 6315153.
2. What are the Factors of 2509?
Answer: Factors of 2509 are 1, 13, 193, 2509. There are 4 integers that are factors of 2509. The greatest factor of 2509 is 2509.
3. What are the Factors of 2517?
Answer: Factors of 2517 are 1, 3, 839, 2517. There are 4 integers that are factors of 2517. The greatest factor of 2517 is 2517.
4. How to Find the LCM of 2509 and 2517?
Answer:
Least Common Multiple of 2509 and 2517 = 6315153
Step 1: Find the prime factorization of 2509
2509 = 13 x 193
Step 2: Find the prime factorization of 2517
2517 = 3 x 839
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 6315153 = 3 x 13 x 193 x 839
Step 4: Therefore, the least common multiple of 2509 and 2517 is 6315153.