Least Common Multiple of 315 and 320

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 315 and 320 the smallest integer that is 20160 that is divisible by both numbers.

Least Common Multiple (LCM) of 315 and 320 is 20160.

LCM(315,320) = 20160

LCM of 315 and 320

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

LCM of:
and

Least Common Multiple of 315 and 320

LCM of 315 and 320 is 20160

Least common multiple can be found by multiplying the highest exponent prime factors of 315 and 320. First we will calculate the prime factors of 315 and 320.

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

Prime Factorization of 320


2 320
2 160
2 80
2 40
2 20
2 10
5 5
1

Prime factors of 320 are 2,5. Prime factorization of 320 in exponential form is:

320 = 26×51

Now multiplying the highest exponent prime factors to calculate the LCM of 315 and 320.

LCM(315,320) = 26×32×51×71
LCM(315,320) = 20160

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

Factors of 320

List of positive integer factors of 320 that divides 320 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320

Least Common Multiple of 315 and 320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 315 and 320, than apply into the LCM equation.

GCF(315,320) = 5
LCM(315,320) = ( 315 × 320) / 5
LCM(315,320) = 100800 / 5
LCM(315,320) = 20160

Properties of LCM 315 and 320

(i) The LCM of 320 and 315 is associative

LCM of 315 and 320 = LCM of 320 and 315

Related Least Common Multiples of 315

Related Least Common Multiples of 320

Frequently Asked Questions on LCM of 315 and 320

1. What is the LCM of 315 and 320?

Answer: LCM of 315 and 320 is 20160.

2. 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.

3. What are the Factors of 320?

Answer: Factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320. There are 14 integers that are factors of 320. The greatest factor of 320 is 320.

4. How to Find the LCM of 315 and 320?

Answer:

Least Common Multiple of 315 and 320 = 20160

Step 1: Find the prime factorization of 315

315 = 3 x 3 x 5 x 7

Step 2: Find the prime factorization of 320

320 = 2 x 2 x 2 x 2 x 2 x 2 x 5

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

LCM = 20160 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 315 and 320 is 20160.