Least Common Multiple of 300 and 306

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 300 and 306 the smallest integer that is 15300 that is divisible by both numbers.

Least Common Multiple (LCM) of 300 and 306 is 15300.

LCM(300,306) = 15300

LCM of 300 and 306

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

LCM of:
and

Least Common Multiple of 300 and 306

LCM of 300 and 306 is 15300

Least common multiple can be found by multiplying the highest exponent prime factors of 300 and 306. First we will calculate the prime factors of 300 and 306.

Prime Factorization of 300


2 300
2 150
3 75
5 25
5 5
1

Prime factors of 300 are 2, 3,5. Prime factorization of 300 in exponential form is:

300 = 22×31×52

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

Now multiplying the highest exponent prime factors to calculate the LCM of 300 and 306.

LCM(300,306) = 22×32×52×171
LCM(300,306) = 15300

Factors of 300

List of positive integer factors of 300 that divides 300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300

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

Least Common Multiple of 300 and 306 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 300 and 306, than apply into the LCM equation.

GCF(300,306) = 6
LCM(300,306) = ( 300 × 306) / 6
LCM(300,306) = 91800 / 6
LCM(300,306) = 15300

Properties of LCM 300 and 306

(i) The LCM of 306 and 300 is associative

LCM of 300 and 306 = LCM of 306 and 300

Related Least Common Multiples of 300

Related Least Common Multiples of 306

Frequently Asked Questions on LCM of 300 and 306

1. What is the LCM of 300 and 306?

Answer: LCM of 300 and 306 is 15300.

2. What are the Factors of 300?

Answer: Factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300. There are 18 integers that are factors of 300. The greatest factor of 300 is 300.

3. 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.

4. How to Find the LCM of 300 and 306?

Answer:

Least Common Multiple of 300 and 306 = 15300

Step 1: Find the prime factorization of 300

300 = 2 x 2 x 3 x 5 x 5

Step 2: Find the prime factorization of 306

306 = 2 x 3 x 3 x 17

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

LCM = 15300 = 2 x 2 x 3 x 3 x 5 x 5 x 17

Step 4: Therefore, the least common multiple of 300 and 306 is 15300.