Least Common Multiple of 306 and 309

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 309 the smallest integer that is 31518 that is divisible by both numbers.

Least Common Multiple (LCM) of 306 and 309 is 31518.

LCM(306,309) = 31518

LCM of 306 and 309

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

LCM of:
and

Least Common Multiple of 306 and 309

LCM of 306 and 309 is 31518

Least common multiple can be found by multiplying the highest exponent prime factors of 306 and 309. First we will calculate the prime factors of 306 and 309.

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 309


3 309
103 103
1

Prime factors of 309 are 3,103. Prime factorization of 309 in exponential form is:

309 = 31×1031

Now multiplying the highest exponent prime factors to calculate the LCM of 306 and 309.

LCM(306,309) = 21×32×171×1031
LCM(306,309) = 31518

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 309

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

1, 3, 103, 309

Least Common Multiple of 306 and 309 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 309, than apply into the LCM equation.

GCF(306,309) = 3
LCM(306,309) = ( 306 × 309) / 3
LCM(306,309) = 94554 / 3
LCM(306,309) = 31518

Properties of LCM 306 and 309

(i) The LCM of 309 and 306 is associative

LCM of 306 and 309 = LCM of 309 and 306

Related Least Common Multiples of 306

Related Least Common Multiples of 309

Frequently Asked Questions on LCM of 306 and 309

1. What is the LCM of 306 and 309?

Answer: LCM of 306 and 309 is 31518.

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 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.

4. How to Find the LCM of 306 and 309?

Answer:

Least Common Multiple of 306 and 309 = 31518

Step 1: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

Step 2: Find the prime factorization of 309

309 = 3 x 103

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

LCM = 31518 = 2 x 3 x 3 x 17 x 103

Step 4: Therefore, the least common multiple of 306 and 309 is 31518.