Least Common Multiple of 306 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 306 and 313 the smallest integer that is 95778 that is divisible by both numbers.

Least Common Multiple (LCM) of 306 and 313 is 95778.

LCM(306,313) = 95778

LCM of 306 and 313

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

LCM of:
and

Least Common Multiple of 306 and 313

LCM of 306 and 313 is 95778

Least common multiple can be found by multiplying the highest exponent prime factors of 306 and 313. First we will calculate the prime factors of 306 and 313.

Prime Factorization of 306


2 306
3 153
3 51
17 17
1

Prime factors of 306 are 2, 3,17. Prime factorization of 306 in exponential form is:

306 = 21×32×171

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 306 and 313.

LCM(306,313) = 21×32×171×3131
LCM(306,313) = 95778

Factors of 306

List of positive integer factors of 306 that divides 306 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306

Factors of 313

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

1, 313

Least Common Multiple of 306 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 306 and 313, than apply into the LCM equation.

GCF(306,313) = 1
LCM(306,313) = ( 306 × 313) / 1
LCM(306,313) = 95778 / 1
LCM(306,313) = 95778

Properties of LCM 306 and 313

(i) The LCM of 313 and 306 is associative

LCM of 306 and 313 = LCM of 313 and 306

Related Least Common Multiples of 306

Related Least Common Multiples of 313

Frequently Asked Questions on LCM of 306 and 313

1. What is the LCM of 306 and 313?

Answer: LCM of 306 and 313 is 95778.

2. What are the Factors of 306?

Answer: Factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306. There are 12 integers that are factors of 306. The greatest factor of 306 is 306.

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 306 and 313?

Answer:

Least Common Multiple of 306 and 313 = 95778

Step 1: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

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 = 95778 = 2 x 3 x 3 x 17 x 313

Step 4: Therefore, the least common multiple of 306 and 313 is 95778.