Least Common Multiple of 300 and 308

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 308 the smallest integer that is 23100 that is divisible by both numbers.

Least Common Multiple (LCM) of 300 and 308 is 23100.

LCM(300,308) = 23100

LCM of 300 and 308

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

LCM of:
and

Least Common Multiple of 300 and 308

LCM of 300 and 308 is 23100

Least common multiple can be found by multiplying the highest exponent prime factors of 300 and 308. First we will calculate the prime factors of 300 and 308.

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 308


2 308
2 154
7 77
11 11
1

Prime factors of 308 are 2, 7,11. Prime factorization of 308 in exponential form is:

308 = 22×71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 300 and 308.

LCM(300,308) = 22×31×52×71×111
LCM(300,308) = 23100

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 308

List of positive integer factors of 308 that divides 308 without a remainder.

1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

Least Common Multiple of 300 and 308 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 308, than apply into the LCM equation.

GCF(300,308) = 4
LCM(300,308) = ( 300 × 308) / 4
LCM(300,308) = 92400 / 4
LCM(300,308) = 23100

Properties of LCM 300 and 308

(i) The LCM of 308 and 300 is associative

LCM of 300 and 308 = LCM of 308 and 300

Related Least Common Multiples of 300

Related Least Common Multiples of 308

Frequently Asked Questions on LCM of 300 and 308

1. What is the LCM of 300 and 308?

Answer: LCM of 300 and 308 is 23100.

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 308?

Answer: Factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308. There are 12 integers that are factors of 308. The greatest factor of 308 is 308.

4. How to Find the LCM of 300 and 308?

Answer:

Least Common Multiple of 300 and 308 = 23100

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 308

308 = 2 x 2 x 7 x 11

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

LCM = 23100 = 2 x 2 x 3 x 5 x 5 x 7 x 11

Step 4: Therefore, the least common multiple of 300 and 308 is 23100.