Least Common Multiple of 303 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 303 and 306 the smallest integer that is 30906 that is divisible by both numbers.

Least Common Multiple (LCM) of 303 and 306 is 30906.

LCM(303,306) = 30906

LCM of 303 and 306

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

LCM of:
and

Least Common Multiple of 303 and 306

LCM of 303 and 306 is 30906

Least common multiple can be found by multiplying the highest exponent prime factors of 303 and 306. First we will calculate the prime factors of 303 and 306.

Prime Factorization of 303


3 303
101 101
1

Prime factors of 303 are 3,101. Prime factorization of 303 in exponential form is:

303 = 31×1011

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 303 and 306.

LCM(303,306) = 21×32×171×1011
LCM(303,306) = 30906

Factors of 303

List of positive integer factors of 303 that divides 303 without a remainder.

1, 3, 101, 303

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 303 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 303 and 306, than apply into the LCM equation.

GCF(303,306) = 3
LCM(303,306) = ( 303 × 306) / 3
LCM(303,306) = 92718 / 3
LCM(303,306) = 30906

Properties of LCM 303 and 306

(i) The LCM of 306 and 303 is associative

LCM of 303 and 306 = LCM of 306 and 303

Related Least Common Multiples of 303

Related Least Common Multiples of 306

Frequently Asked Questions on LCM of 303 and 306

1. What is the LCM of 303 and 306?

Answer: LCM of 303 and 306 is 30906.

2. What are the Factors of 303?

Answer: Factors of 303 are 1, 3, 101, 303. There are 4 integers that are factors of 303. The greatest factor of 303 is 303.

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 303 and 306?

Answer:

Least Common Multiple of 303 and 306 = 30906

Step 1: Find the prime factorization of 303

303 = 3 x 101

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 = 30906 = 2 x 3 x 3 x 17 x 101

Step 4: Therefore, the least common multiple of 303 and 306 is 30906.