Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7709 and 7713 the smallest integer that is 59459517 that is divisible by both numbers.
Least Common Multiple (LCM) of 7709 and 7713 is 59459517.
LCM(7709,7713) = 59459517
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 7709 and 7713. First we will calculate the prime factors of 7709 and 7713.
Prime Factorization of 7709
13 | 7709 |
593 | 593 |
1 |
Prime factors of 7709 are 13,593. Prime factorization of 7709 in exponential form is:
7709 = 131×5931
Prime Factorization of 7713
3 | 7713 |
3 | 2571 |
857 | 857 |
1 |
Prime factors of 7713 are 3,857. Prime factorization of 7713 in exponential form is:
7713 = 32×8571
Now multiplying the highest exponent prime factors to calculate the LCM of 7709 and 7713.
LCM(7709,7713) = 32×131×5931×8571
LCM(7709,7713) = 59459517
Factors of 7709
List of positive integer factors of 7709 that divides 7709 without a remainder.
1, 13, 593, 7709
Factors of 7713
List of positive integer factors of 7713 that divides 7713 without a remainder.
1, 3, 9, 857, 2571, 7713
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7709 and 7713, than apply into the LCM equation.
GCF(7709,7713) = 1
LCM(7709,7713) = ( 7709 × 7713) / 1
LCM(7709,7713) = 59459517 / 1
LCM(7709,7713) = 59459517
(i) The LCM of 7713 and 7709 is associative
LCM of 7709 and 7713 = LCM of 7713 and 7709
1. What is the LCM of 7709 and 7713?
Answer: LCM of 7709 and 7713 is 59459517.
2. What are the Factors of 7709?
Answer: Factors of 7709 are 1, 13, 593, 7709. There are 4 integers that are factors of 7709. The greatest factor of 7709 is 7709.
3. What are the Factors of 7713?
Answer: Factors of 7713 are 1, 3, 9, 857, 2571, 7713. There are 6 integers that are factors of 7713. The greatest factor of 7713 is 7713.
4. How to Find the LCM of 7709 and 7713?
Answer:
Least Common Multiple of 7709 and 7713 = 59459517
Step 1: Find the prime factorization of 7709
7709 = 13 x 593
Step 2: Find the prime factorization of 7713
7713 = 3 x 3 x 857
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 59459517 = 3 x 3 x 13 x 593 x 857
Step 4: Therefore, the least common multiple of 7709 and 7713 is 59459517.