Least Common Multiple of 12304 and 12312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 12304 and 12312 the smallest integer that is 18935856 that is divisible by both numbers.

Least Common Multiple (LCM) of 12304 and 12312 is 18935856.

LCM(12304,12312) = 18935856

LCM of 12304 and 12312

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

LCM of:
and

Least Common Multiple of 12304 and 12312

LCM of 12304 and 12312 is 18935856

Least common multiple can be found by multiplying the highest exponent prime factors of 12304 and 12312. First we will calculate the prime factors of 12304 and 12312.

Prime Factorization of 12304


2 12304
2 6152
2 3076
2 1538
769 769
1

Prime factors of 12304 are 2,769. Prime factorization of 12304 in exponential form is:

12304 = 24×7691

Prime Factorization of 12312


2 12312
2 6156
2 3078
3 1539
3 513
3 171
3 57
19 19
1

Prime factors of 12312 are 2, 3,19. Prime factorization of 12312 in exponential form is:

12312 = 23×34×191

Now multiplying the highest exponent prime factors to calculate the LCM of 12304 and 12312.

LCM(12304,12312) = 24×34×191×7691
LCM(12304,12312) = 18935856

Factors of 12304

List of positive integer factors of 12304 that divides 12304 without a remainder.

1, 2, 4, 8, 16, 769, 1538, 3076, 6152, 12304

Factors of 12312

List of positive integer factors of 12312 that divides 12312 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 27, 36, 38, 54, 57, 72, 76, 81, 108, 114, 152, 162, 171, 216, 228, 324, 342, 456, 513, 648, 684, 1026, 1368, 1539, 2052, 3078, 4104, 6156, 12312

Least Common Multiple of 12304 and 12312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12304 and 12312, than apply into the LCM equation.

GCF(12304,12312) = 8
LCM(12304,12312) = ( 12304 × 12312) / 8
LCM(12304,12312) = 151486848 / 8
LCM(12304,12312) = 18935856

Properties of LCM 12304 and 12312

(i) The LCM of 12312 and 12304 is associative

LCM of 12304 and 12312 = LCM of 12312 and 12304

Related Least Common Multiples of 12304

Related Least Common Multiples of 12312

Frequently Asked Questions on LCM of 12304 and 12312

1. What is the LCM of 12304 and 12312?

Answer: LCM of 12304 and 12312 is 18935856.

2. What are the Factors of 12304?

Answer: Factors of 12304 are 1, 2, 4, 8, 16, 769, 1538, 3076, 6152, 12304. There are 10 integers that are factors of 12304. The greatest factor of 12304 is 12304.

3. What are the Factors of 12312?

Answer: Factors of 12312 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 19, 24, 27, 36, 38, 54, 57, 72, 76, 81, 108, 114, 152, 162, 171, 216, 228, 324, 342, 456, 513, 648, 684, 1026, 1368, 1539, 2052, 3078, 4104, 6156, 12312. There are 40 integers that are factors of 12312. The greatest factor of 12312 is 12312.

4. How to Find the LCM of 12304 and 12312?

Answer:

Least Common Multiple of 12304 and 12312 = 18935856

Step 1: Find the prime factorization of 12304

12304 = 2 x 2 x 2 x 2 x 769

Step 2: Find the prime factorization of 12312

12312 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 19

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

LCM = 18935856 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 19 x 769

Step 4: Therefore, the least common multiple of 12304 and 12312 is 18935856.