Least Common Multiple of 300 and 304

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 304 the smallest integer that is 22800 that is divisible by both numbers.

Least Common Multiple (LCM) of 300 and 304 is 22800.

LCM(300,304) = 22800

LCM of 300 and 304

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

LCM of:
and

Least Common Multiple of 300 and 304

LCM of 300 and 304 is 22800

Least common multiple can be found by multiplying the highest exponent prime factors of 300 and 304. First we will calculate the prime factors of 300 and 304.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 300 and 304.

LCM(300,304) = 24×31×52×191
LCM(300,304) = 22800

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 304

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

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

Least Common Multiple of 300 and 304 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 304, than apply into the LCM equation.

GCF(300,304) = 4
LCM(300,304) = ( 300 × 304) / 4
LCM(300,304) = 91200 / 4
LCM(300,304) = 22800

Properties of LCM 300 and 304

(i) The LCM of 304 and 300 is associative

LCM of 300 and 304 = LCM of 304 and 300

Related Least Common Multiples of 300

Related Least Common Multiples of 304

Frequently Asked Questions on LCM of 300 and 304

1. What is the LCM of 300 and 304?

Answer: LCM of 300 and 304 is 22800.

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 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.

4. How to Find the LCM of 300 and 304?

Answer:

Least Common Multiple of 300 and 304 = 22800

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 304

304 = 2 x 2 x 2 x 2 x 19

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

LCM = 22800 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 19

Step 4: Therefore, the least common multiple of 300 and 304 is 22800.