Least Common Multiple of 304 and 312

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 304 and 312 the smallest integer that is 11856 that is divisible by both numbers.

Least Common Multiple (LCM) of 304 and 312 is 11856.

LCM(304,312) = 11856

LCM of 304 and 312

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

LCM of:
and

Least Common Multiple of 304 and 312

LCM of 304 and 312 is 11856

Least common multiple can be found by multiplying the highest exponent prime factors of 304 and 312. First we will calculate the prime factors of 304 and 312.

Prime Factorization of 304


2 304
2 152
2 76
2 38
19 19
1

Prime factors of 304 are 2,19. Prime factorization of 304 in exponential form is:

304 = 24×191

Prime Factorization of 312


2 312
2 156
2 78
3 39
13 13
1

Prime factors of 312 are 2, 3,13. Prime factorization of 312 in exponential form is:

312 = 23×31×131

Now multiplying the highest exponent prime factors to calculate the LCM of 304 and 312.

LCM(304,312) = 24×31×131×191
LCM(304,312) = 11856

Factors of 304

List of positive integer factors of 304 that divides 304 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 152, 304

Factors of 312

List of positive integer factors of 312 that divides 312 without a remainder.

1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

Least Common Multiple of 304 and 312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 304 and 312, than apply into the LCM equation.

GCF(304,312) = 8
LCM(304,312) = ( 304 × 312) / 8
LCM(304,312) = 94848 / 8
LCM(304,312) = 11856

Properties of LCM 304 and 312

(i) The LCM of 312 and 304 is associative

LCM of 304 and 312 = LCM of 312 and 304

Related Least Common Multiples of 304

Related Least Common Multiples of 312

Frequently Asked Questions on LCM of 304 and 312

1. What is the LCM of 304 and 312?

Answer: LCM of 304 and 312 is 11856.

2. What are the Factors of 304?

Answer: Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304. There are 10 integers that are factors of 304. The greatest factor of 304 is 304.

3. What are the Factors of 312?

Answer: Factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312. There are 16 integers that are factors of 312. The greatest factor of 312 is 312.

4. How to Find the LCM of 304 and 312?

Answer:

Least Common Multiple of 304 and 312 = 11856

Step 1: Find the prime factorization of 304

304 = 2 x 2 x 2 x 2 x 19

Step 2: Find the prime factorization of 312

312 = 2 x 2 x 2 x 3 x 13

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

LCM = 11856 = 2 x 2 x 2 x 2 x 3 x 13 x 19

Step 4: Therefore, the least common multiple of 304 and 312 is 11856.