Least Common Multiple of 312 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 312 and 320 the smallest integer that is 12480 that is divisible by both numbers.

Least Common Multiple (LCM) of 312 and 320 is 12480.

LCM(312,320) = 12480

LCM of 312 and 320

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

LCM of:
and

Least Common Multiple of 312 and 320

LCM of 312 and 320 is 12480

Least common multiple can be found by multiplying the highest exponent prime factors of 312 and 320. First we will calculate the prime factors of 312 and 320.

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 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 312 and 320.

LCM(312,320) = 26×31×51×131
LCM(312,320) = 12480

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 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 312 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 312 and 320, than apply into the LCM equation.

GCF(312,320) = 8
LCM(312,320) = ( 312 × 320) / 8
LCM(312,320) = 99840 / 8
LCM(312,320) = 12480

Properties of LCM 312 and 320

(i) The LCM of 320 and 312 is associative

LCM of 312 and 320 = LCM of 320 and 312

Related Least Common Multiples of 312

Related Least Common Multiples of 320

Frequently Asked Questions on LCM of 312 and 320

1. What is the LCM of 312 and 320?

Answer: LCM of 312 and 320 is 12480.

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 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 312 and 320?

Answer:

Least Common Multiple of 312 and 320 = 12480

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 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 = 12480 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 13

Step 4: Therefore, the least common multiple of 312 and 320 is 12480.