Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 9309 and 9314 the smallest integer that is 86704026 that is divisible by both numbers.
Least Common Multiple (LCM) of 9309 and 9314 is 86704026.
LCM(9309,9314) = 86704026
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 9309 and 9314. First we will calculate the prime factors of 9309 and 9314.
Prime Factorization of 9309
3 | 9309 |
29 | 3103 |
107 | 107 |
1 |
Prime factors of 9309 are 3, 29,107. Prime factorization of 9309 in exponential form is:
9309 = 31×291×1071
Prime Factorization of 9314
2 | 9314 |
4657 | 4657 |
1 |
Prime factors of 9314 are 2,4657. Prime factorization of 9314 in exponential form is:
9314 = 21×46571
Now multiplying the highest exponent prime factors to calculate the LCM of 9309 and 9314.
LCM(9309,9314) = 21×31×291×1071×46571
LCM(9309,9314) = 86704026
Factors of 9309
List of positive integer factors of 9309 that divides 9309 without a remainder.
1, 3, 29, 87, 107, 321, 3103, 9309
Factors of 9314
List of positive integer factors of 9314 that divides 9314 without a remainder.
1, 2, 4657, 9314
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9309 and 9314, than apply into the LCM equation.
GCF(9309,9314) = 1
LCM(9309,9314) = ( 9309 × 9314) / 1
LCM(9309,9314) = 86704026 / 1
LCM(9309,9314) = 86704026
(i) The LCM of 9314 and 9309 is associative
LCM of 9309 and 9314 = LCM of 9314 and 9309
1. What is the LCM of 9309 and 9314?
Answer: LCM of 9309 and 9314 is 86704026.
2. What are the Factors of 9309?
Answer: Factors of 9309 are 1, 3, 29, 87, 107, 321, 3103, 9309. There are 8 integers that are factors of 9309. The greatest factor of 9309 is 9309.
3. What are the Factors of 9314?
Answer: Factors of 9314 are 1, 2, 4657, 9314. There are 4 integers that are factors of 9314. The greatest factor of 9314 is 9314.
4. How to Find the LCM of 9309 and 9314?
Answer:
Least Common Multiple of 9309 and 9314 = 86704026
Step 1: Find the prime factorization of 9309
9309 = 3 x 29 x 107
Step 2: Find the prime factorization of 9314
9314 = 2 x 4657
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 86704026 = 2 x 3 x 29 x 107 x 4657
Step 4: Therefore, the least common multiple of 9309 and 9314 is 86704026.