Least Common Multiple of 312 and 315

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 312 and 315 the smallest integer that is 32760 that is divisible by both numbers.

Least Common Multiple (LCM) of 312 and 315 is 32760.

LCM(312,315) = 32760

LCM of 312 and 315

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

LCM of:
and

Least Common Multiple of 312 and 315

LCM of 312 and 315 is 32760

Least common multiple can be found by multiplying the highest exponent prime factors of 312 and 315. First we will calculate the prime factors of 312 and 315.

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

Prime Factorization of 315


3 315
3 105
5 35
7 7
1

Prime factors of 315 are 3, 5,7. Prime factorization of 315 in exponential form is:

315 = 32×51×71

Now multiplying the highest exponent prime factors to calculate the LCM of 312 and 315.

LCM(312,315) = 23×32×51×71×131
LCM(312,315) = 32760

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

Factors of 315

List of positive integer factors of 315 that divides 315 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315

Least Common Multiple of 312 and 315 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 312 and 315, than apply into the LCM equation.

GCF(312,315) = 3
LCM(312,315) = ( 312 × 315) / 3
LCM(312,315) = 98280 / 3
LCM(312,315) = 32760

Properties of LCM 312 and 315

(i) The LCM of 315 and 312 is associative

LCM of 312 and 315 = LCM of 315 and 312

Related Least Common Multiples of 312

Related Least Common Multiples of 315

Frequently Asked Questions on LCM of 312 and 315

1. What is the LCM of 312 and 315?

Answer: LCM of 312 and 315 is 32760.

2. 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.

3. What are the Factors of 315?

Answer: Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. There are 12 integers that are factors of 315. The greatest factor of 315 is 315.

4. How to Find the LCM of 312 and 315?

Answer:

Least Common Multiple of 312 and 315 = 32760

Step 1: Find the prime factorization of 312

312 = 2 x 2 x 2 x 3 x 13

Step 2: Find the prime factorization of 315

315 = 3 x 3 x 5 x 7

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

LCM = 32760 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 312 and 315 is 32760.