Least Common Multiple of 306 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 306 and 312 the smallest integer that is 15912 that is divisible by both numbers.

Least Common Multiple (LCM) of 306 and 312 is 15912.

LCM(306,312) = 15912

LCM of 306 and 312

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

LCM of:
and

Least Common Multiple of 306 and 312

LCM of 306 and 312 is 15912

Least common multiple can be found by multiplying the highest exponent prime factors of 306 and 312. First we will calculate the prime factors of 306 and 312.

Prime Factorization of 306


2 306
3 153
3 51
17 17
1

Prime factors of 306 are 2, 3,17. Prime factorization of 306 in exponential form is:

306 = 21×32×171

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 306 and 312.

LCM(306,312) = 23×32×131×171
LCM(306,312) = 15912

Factors of 306

List of positive integer factors of 306 that divides 306 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306

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 306 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 306 and 312, than apply into the LCM equation.

GCF(306,312) = 6
LCM(306,312) = ( 306 × 312) / 6
LCM(306,312) = 95472 / 6
LCM(306,312) = 15912

Properties of LCM 306 and 312

(i) The LCM of 312 and 306 is associative

LCM of 306 and 312 = LCM of 312 and 306

Related Least Common Multiples of 306

Related Least Common Multiples of 312

Frequently Asked Questions on LCM of 306 and 312

1. What is the LCM of 306 and 312?

Answer: LCM of 306 and 312 is 15912.

2. What are the Factors of 306?

Answer: Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. There are 12 integers that are factors of 306. The greatest factor of 306 is 306.

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 306 and 312?

Answer:

Least Common Multiple of 306 and 312 = 15912

Step 1: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

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 = 15912 = 2 x 2 x 2 x 3 x 3 x 13 x 17

Step 4: Therefore, the least common multiple of 306 and 312 is 15912.