Least Common Multiple of 309 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 309 and 315 the smallest integer that is 32445 that is divisible by both numbers.

Least Common Multiple (LCM) of 309 and 315 is 32445.

LCM(309,315) = 32445

LCM of 309 and 315

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

LCM of:
and

Least Common Multiple of 309 and 315

LCM of 309 and 315 is 32445

Least common multiple can be found by multiplying the highest exponent prime factors of 309 and 315. First we will calculate the prime factors of 309 and 315.

Prime Factorization of 309


3 309
103 103
1

Prime factors of 309 are 3,103. Prime factorization of 309 in exponential form is:

309 = 31×1031

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 309 and 315.

LCM(309,315) = 32×51×71×1031
LCM(309,315) = 32445

Factors of 309

List of positive integer factors of 309 that divides 309 without a remainder.

1, 3, 103, 309

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 309 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 309 and 315, than apply into the LCM equation.

GCF(309,315) = 3
LCM(309,315) = ( 309 × 315) / 3
LCM(309,315) = 97335 / 3
LCM(309,315) = 32445

Properties of LCM 309 and 315

(i) The LCM of 315 and 309 is associative

LCM of 309 and 315 = LCM of 315 and 309

Related Least Common Multiples of 309

Related Least Common Multiples of 315

Frequently Asked Questions on LCM of 309 and 315

1. What is the LCM of 309 and 315?

Answer: LCM of 309 and 315 is 32445.

2. What are the Factors of 309?

Answer: Factors of 309 are 1, 3, 103, 309. There are 4 integers that are factors of 309. The greatest factor of 309 is 309.

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 309 and 315?

Answer:

Least Common Multiple of 309 and 315 = 32445

Step 1: Find the prime factorization of 309

309 = 3 x 103

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 = 32445 = 3 x 3 x 5 x 7 x 103

Step 4: Therefore, the least common multiple of 309 and 315 is 32445.