Least Common Multiple of 9309 and 9312

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 9312 the smallest integer that is 28895136 that is divisible by both numbers.

Least Common Multiple (LCM) of 9309 and 9312 is 28895136.

LCM(9309,9312) = 28895136

LCM of 9309 and 9312

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 9309 and 9312

LCM of 9309 and 9312 is 28895136

Least common multiple can be found by multiplying the highest exponent prime factors of 9309 and 9312. First we will calculate the prime factors of 9309 and 9312.

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 9312


2 9312
2 4656
2 2328
2 1164
2 582
3 291
97 97
1

Prime factors of 9312 are 2, 3,97. Prime factorization of 9312 in exponential form is:

9312 = 25×31×971

Now multiplying the highest exponent prime factors to calculate the LCM of 9309 and 9312.

LCM(9309,9312) = 25×31×291×971×1071
LCM(9309,9312) = 28895136

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 9312

List of positive integer factors of 9312 that divides 9312 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 97, 194, 291, 388, 582, 776, 1164, 1552, 2328, 3104, 4656, 9312

Least Common Multiple of 9309 and 9312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9309 and 9312, than apply into the LCM equation.

GCF(9309,9312) = 3
LCM(9309,9312) = ( 9309 × 9312) / 3
LCM(9309,9312) = 86685408 / 3
LCM(9309,9312) = 28895136

Properties of LCM 9309 and 9312

(i) The LCM of 9312 and 9309 is associative

LCM of 9309 and 9312 = LCM of 9312 and 9309

Related Least Common Multiples of 9309

Related Least Common Multiples of 9312

Frequently Asked Questions on LCM of 9309 and 9312

1. What is the LCM of 9309 and 9312?

Answer: LCM of 9309 and 9312 is 28895136.

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 9312?

Answer: Factors of 9312 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 97, 194, 291, 388, 582, 776, 1164, 1552, 2328, 3104, 4656, 9312. There are 24 integers that are factors of 9312. The greatest factor of 9312 is 9312.

4. How to Find the LCM of 9309 and 9312?

Answer:

Least Common Multiple of 9309 and 9312 = 28895136

Step 1: Find the prime factorization of 9309

9309 = 3 x 29 x 107

Step 2: Find the prime factorization of 9312

9312 = 2 x 2 x 2 x 2 x 2 x 3 x 97

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 28895136 = 2 x 2 x 2 x 2 x 2 x 3 x 29 x 97 x 107

Step 4: Therefore, the least common multiple of 9309 and 9312 is 28895136.