Least Common Multiple of 309 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 309 and 313 the smallest integer that is 96717 that is divisible by both numbers.

Least Common Multiple (LCM) of 309 and 313 is 96717.

LCM(309,313) = 96717

LCM of 309 and 313

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

LCM of:
and

Least Common Multiple of 309 and 313

LCM of 309 and 313 is 96717

Least common multiple can be found by multiplying the highest exponent prime factors of 309 and 313. First we will calculate the prime factors of 309 and 313.

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 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 309 and 313.

LCM(309,313) = 31×1031×3131
LCM(309,313) = 96717

Factors of 309

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

1, 3, 103, 309

Factors of 313

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

1, 313

Least Common Multiple of 309 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 309 and 313, than apply into the LCM equation.

GCF(309,313) = 1
LCM(309,313) = ( 309 × 313) / 1
LCM(309,313) = 96717 / 1
LCM(309,313) = 96717

Properties of LCM 309 and 313

(i) The LCM of 313 and 309 is associative

LCM of 309 and 313 = LCM of 313 and 309

Related Least Common Multiples of 309

Related Least Common Multiples of 313

Frequently Asked Questions on LCM of 309 and 313

1. What is the LCM of 309 and 313?

Answer: LCM of 309 and 313 is 96717.

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 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 309 and 313?

Answer:

Least Common Multiple of 309 and 313 = 96717

Step 1: Find the prime factorization of 309

309 = 3 x 103

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 = 96717 = 3 x 103 x 313

Step 4: Therefore, the least common multiple of 309 and 313 is 96717.