Least Common Multiple of 9312 and 9315

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9312 and 9315 the smallest integer that is 28913760 that is divisible by both numbers.

Least Common Multiple (LCM) of 9312 and 9315 is 28913760.

LCM(9312,9315) = 28913760

LCM of 9312 and 9315

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

LCM of:
and

Least Common Multiple of 9312 and 9315

LCM of 9312 and 9315 is 28913760

Least common multiple can be found by multiplying the highest exponent prime factors of 9312 and 9315. First we will calculate the prime factors of 9312 and 9315.

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

Prime Factorization of 9315


3 9315
3 3105
3 1035
3 345
5 115
23 23
1

Prime factors of 9315 are 3, 5,23. Prime factorization of 9315 in exponential form is:

9315 = 34×51×231

Now multiplying the highest exponent prime factors to calculate the LCM of 9312 and 9315.

LCM(9312,9315) = 25×34×51×231×971
LCM(9312,9315) = 28913760

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

Factors of 9315

List of positive integer factors of 9315 that divides 9315 without a remainder.

1, 3, 5, 9, 15, 23, 27, 45, 69, 81, 115, 135, 207, 345, 405, 621, 1035, 1863, 3105, 9315

Least Common Multiple of 9312 and 9315 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9312 and 9315, than apply into the LCM equation.

GCF(9312,9315) = 3
LCM(9312,9315) = ( 9312 × 9315) / 3
LCM(9312,9315) = 86741280 / 3
LCM(9312,9315) = 28913760

Properties of LCM 9312 and 9315

(i) The LCM of 9315 and 9312 is associative

LCM of 9312 and 9315 = LCM of 9315 and 9312

Related Least Common Multiples of 9312

Related Least Common Multiples of 9315

Frequently Asked Questions on LCM of 9312 and 9315

1. What is the LCM of 9312 and 9315?

Answer: LCM of 9312 and 9315 is 28913760.

2. 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.

3. What are the Factors of 9315?

Answer: Factors of 9315 are 1, 3, 5, 9, 15, 23, 27, 45, 69, 81, 115, 135, 207, 345, 405, 621, 1035, 1863, 3105, 9315. There are 20 integers that are factors of 9315. The greatest factor of 9315 is 9315.

4. How to Find the LCM of 9312 and 9315?

Answer:

Least Common Multiple of 9312 and 9315 = 28913760

Step 1: Find the prime factorization of 9312

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

Step 2: Find the prime factorization of 9315

9315 = 3 x 3 x 3 x 3 x 5 x 23

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

LCM = 28913760 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 23 x 97

Step 4: Therefore, the least common multiple of 9312 and 9315 is 28913760.