Least Common Multiple of 312 and 317

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 317 the smallest integer that is 98904 that is divisible by both numbers.

Least Common Multiple (LCM) of 312 and 317 is 98904.

LCM(312,317) = 98904

LCM of 312 and 317

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

LCM of:
and

Least Common Multiple of 312 and 317

LCM of 312 and 317 is 98904

Least common multiple can be found by multiplying the highest exponent prime factors of 312 and 317. First we will calculate the prime factors of 312 and 317.

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 317


317 317
1

Prime factors of 317 are 317. Prime factorization of 317 in exponential form is:

317 = 3171

Now multiplying the highest exponent prime factors to calculate the LCM of 312 and 317.

LCM(312,317) = 23×31×131×3171
LCM(312,317) = 98904

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 317

List of positive integer factors of 317 that divides 317 without a remainder.

1, 317

Least Common Multiple of 312 and 317 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 317, than apply into the LCM equation.

GCF(312,317) = 1
LCM(312,317) = ( 312 × 317) / 1
LCM(312,317) = 98904 / 1
LCM(312,317) = 98904

Properties of LCM 312 and 317

(i) The LCM of 317 and 312 is associative

LCM of 312 and 317 = LCM of 317 and 312

Related Least Common Multiples of 312

Related Least Common Multiples of 317

Frequently Asked Questions on LCM of 312 and 317

1. What is the LCM of 312 and 317?

Answer: LCM of 312 and 317 is 98904.

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 317?

Answer: Factors of 317 are 1, 317. There are 2 integers that are factors of 317. The greatest factor of 317 is 317.

4. How to Find the LCM of 312 and 317?

Answer:

Least Common Multiple of 312 and 317 = 98904

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 317

317 = 317

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

LCM = 98904 = 2 x 2 x 2 x 3 x 13 x 317

Step 4: Therefore, the least common multiple of 312 and 317 is 98904.