Least Common Multiple of 304 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 304 and 306 the smallest integer that is 46512 that is divisible by both numbers.

Least Common Multiple (LCM) of 304 and 306 is 46512.

LCM(304,306) = 46512

LCM of 304 and 306

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

LCM of:
and

Least Common Multiple of 304 and 306

LCM of 304 and 306 is 46512

Least common multiple can be found by multiplying the highest exponent prime factors of 304 and 306. First we will calculate the prime factors of 304 and 306.

Prime Factorization of 304


2 304
2 152
2 76
2 38
19 19
1

Prime factors of 304 are 2,19. Prime factorization of 304 in exponential form is:

304 = 24×191

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 304 and 306.

LCM(304,306) = 24×32×171×191
LCM(304,306) = 46512

Factors of 304

List of positive integer factors of 304 that divides 304 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 152, 304

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 304 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 304 and 306, than apply into the LCM equation.

GCF(304,306) = 2
LCM(304,306) = ( 304 × 306) / 2
LCM(304,306) = 93024 / 2
LCM(304,306) = 46512

Properties of LCM 304 and 306

(i) The LCM of 306 and 304 is associative

LCM of 304 and 306 = LCM of 306 and 304

Related Least Common Multiples of 304

Related Least Common Multiples of 306

Frequently Asked Questions on LCM of 304 and 306

1. What is the LCM of 304 and 306?

Answer: LCM of 304 and 306 is 46512.

2. What are the Factors of 304?

Answer: Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304. There are 10 integers that are factors of 304. The greatest factor of 304 is 304.

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 304 and 306?

Answer:

Least Common Multiple of 304 and 306 = 46512

Step 1: Find the prime factorization of 304

304 = 2 x 2 x 2 x 2 x 19

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 = 46512 = 2 x 2 x 2 x 2 x 3 x 3 x 17 x 19

Step 4: Therefore, the least common multiple of 304 and 306 is 46512.