Least Common Multiple of 312 and 313

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 313 the smallest integer that is 97656 that is divisible by both numbers.

Least Common Multiple (LCM) of 312 and 313 is 97656.

LCM(312,313) = 97656

LCM of 312 and 313

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

LCM of:
and

Least Common Multiple of 312 and 313

LCM of 312 and 313 is 97656

Least common multiple can be found by multiplying the highest exponent prime factors of 312 and 313. First we will calculate the prime factors of 312 and 313.

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 313


313 313
1

Prime factors of 313 are 313. Prime factorization of 313 in exponential form is:

313 = 3131

Now multiplying the highest exponent prime factors to calculate the LCM of 312 and 313.

LCM(312,313) = 23×31×131×3131
LCM(312,313) = 97656

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 313

List of positive integer factors of 313 that divides 313 without a remainder.

1, 313

Least Common Multiple of 312 and 313 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 313, than apply into the LCM equation.

GCF(312,313) = 1
LCM(312,313) = ( 312 × 313) / 1
LCM(312,313) = 97656 / 1
LCM(312,313) = 97656

Properties of LCM 312 and 313

(i) The LCM of 313 and 312 is associative

LCM of 312 and 313 = LCM of 313 and 312

Related Least Common Multiples of 312

Related Least Common Multiples of 313

Frequently Asked Questions on LCM of 312 and 313

1. What is the LCM of 312 and 313?

Answer: LCM of 312 and 313 is 97656.

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 313?

Answer: Factors of 313 are 1, 313. There are 2 integers that are factors of 313. The greatest factor of 313 is 313.

4. How to Find the LCM of 312 and 313?

Answer:

Least Common Multiple of 312 and 313 = 97656

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 313

313 = 313

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

LCM = 97656 = 2 x 2 x 2 x 3 x 13 x 313

Step 4: Therefore, the least common multiple of 312 and 313 is 97656.