Least Common Multiple of 308 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 308 and 315 the smallest integer that is 13860 that is divisible by both numbers.

Least Common Multiple (LCM) of 308 and 315 is 13860.

LCM(308,315) = 13860

LCM of 308 and 315

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

LCM of:
and

Least Common Multiple of 308 and 315

LCM of 308 and 315 is 13860

Least common multiple can be found by multiplying the highest exponent prime factors of 308 and 315. First we will calculate the prime factors of 308 and 315.

Prime Factorization of 308


2 308
2 154
7 77
11 11
1

Prime factors of 308 are 2, 7,11. Prime factorization of 308 in exponential form is:

308 = 22×71×111

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 308 and 315.

LCM(308,315) = 22×32×51×71×111
LCM(308,315) = 13860

Factors of 308

List of positive integer factors of 308 that divides 308 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

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 308 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 308 and 315, than apply into the LCM equation.

GCF(308,315) = 7
LCM(308,315) = ( 308 × 315) / 7
LCM(308,315) = 97020 / 7
LCM(308,315) = 13860

Properties of LCM 308 and 315

(i) The LCM of 315 and 308 is associative

LCM of 308 and 315 = LCM of 315 and 308

Related Least Common Multiples of 308

Related Least Common Multiples of 315

Frequently Asked Questions on LCM of 308 and 315

1. What is the LCM of 308 and 315?

Answer: LCM of 308 and 315 is 13860.

2. What are the Factors of 308?

Answer: Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308. There are 12 integers that are factors of 308. The greatest factor of 308 is 308.

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 308 and 315?

Answer:

Least Common Multiple of 308 and 315 = 13860

Step 1: Find the prime factorization of 308

308 = 2 x 2 x 7 x 11

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 = 13860 = 2 x 2 x 3 x 3 x 5 x 7 x 11

Step 4: Therefore, the least common multiple of 308 and 315 is 13860.