Least Common Multiple of 12300 and 12305

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 12300 and 12305 the smallest integer that is 30270300 that is divisible by both numbers.

Least Common Multiple (LCM) of 12300 and 12305 is 30270300.

LCM(12300,12305) = 30270300

LCM of 12300 and 12305

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

LCM of:
and

Least Common Multiple of 12300 and 12305

LCM of 12300 and 12305 is 30270300

Least common multiple can be found by multiplying the highest exponent prime factors of 12300 and 12305. First we will calculate the prime factors of 12300 and 12305.

Prime Factorization of 12300


2 12300
2 6150
3 3075
5 1025
5 205
41 41
1

Prime factors of 12300 are 2, 3, 5,41. Prime factorization of 12300 in exponential form is:

12300 = 22×31×52×411

Prime Factorization of 12305


5 12305
23 2461
107 107
1

Prime factors of 12305 are 5, 23,107. Prime factorization of 12305 in exponential form is:

12305 = 51×231×1071

Now multiplying the highest exponent prime factors to calculate the LCM of 12300 and 12305.

LCM(12300,12305) = 22×31×52×231×411×1071
LCM(12300,12305) = 30270300

Factors of 12300

List of positive integer factors of 12300 that divides 12300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 41, 50, 60, 75, 82, 100, 123, 150, 164, 205, 246, 300, 410, 492, 615, 820, 1025, 1230, 2050, 2460, 3075, 4100, 6150, 12300

Factors of 12305

List of positive integer factors of 12305 that divides 12305 without a remainder.

1, 5, 23, 107, 115, 535, 2461, 12305

Least Common Multiple of 12300 and 12305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12300 and 12305, than apply into the LCM equation.

GCF(12300,12305) = 5
LCM(12300,12305) = ( 12300 × 12305) / 5
LCM(12300,12305) = 151351500 / 5
LCM(12300,12305) = 30270300

Properties of LCM 12300 and 12305

(i) The LCM of 12305 and 12300 is associative

LCM of 12300 and 12305 = LCM of 12305 and 12300

Related Least Common Multiples of 12300

Related Least Common Multiples of 12305

Frequently Asked Questions on LCM of 12300 and 12305

1. What is the LCM of 12300 and 12305?

Answer: LCM of 12300 and 12305 is 30270300.

2. What are the Factors of 12300?

Answer: Factors of 12300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 41, 50, 60, 75, 82, 100, 123, 150, 164, 205, 246, 300, 410, 492, 615, 820, 1025, 1230, 2050, 2460, 3075, 4100, 6150, 12300. There are 36 integers that are factors of 12300. The greatest factor of 12300 is 12300.

3. What are the Factors of 12305?

Answer: Factors of 12305 are 1, 5, 23, 107, 115, 535, 2461, 12305. There are 8 integers that are factors of 12305. The greatest factor of 12305 is 12305.

4. How to Find the LCM of 12300 and 12305?

Answer:

Least Common Multiple of 12300 and 12305 = 30270300

Step 1: Find the prime factorization of 12300

12300 = 2 x 2 x 3 x 5 x 5 x 41

Step 2: Find the prime factorization of 12305

12305 = 5 x 23 x 107

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

LCM = 30270300 = 2 x 2 x 3 x 5 x 5 x 23 x 41 x 107

Step 4: Therefore, the least common multiple of 12300 and 12305 is 30270300.