Least Common Multiple of 12200 and 12205

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 12200 and 12205 the smallest integer that is 29780200 that is divisible by both numbers.

Least Common Multiple (LCM) of 12200 and 12205 is 29780200.

LCM(12200,12205) = 29780200

LCM of 12200 and 12205

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

LCM of:
and

Least Common Multiple of 12200 and 12205

LCM of 12200 and 12205 is 29780200

Least common multiple can be found by multiplying the highest exponent prime factors of 12200 and 12205. First we will calculate the prime factors of 12200 and 12205.

Prime Factorization of 12200


2 12200
2 6100
2 3050
5 1525
5 305
61 61
1

Prime factors of 12200 are 2, 5,61. Prime factorization of 12200 in exponential form is:

12200 = 23×52×611

Prime Factorization of 12205


5 12205
2441 2441
1

Prime factors of 12205 are 5,2441. Prime factorization of 12205 in exponential form is:

12205 = 51×24411

Now multiplying the highest exponent prime factors to calculate the LCM of 12200 and 12205.

LCM(12200,12205) = 23×52×611×24411
LCM(12200,12205) = 29780200

Factors of 12200

List of positive integer factors of 12200 that divides 12200 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 61, 100, 122, 200, 244, 305, 488, 610, 1220, 1525, 2440, 3050, 6100, 12200

Factors of 12205

List of positive integer factors of 12205 that divides 12205 without a remainder.

1, 5, 2441, 12205

Least Common Multiple of 12200 and 12205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12200 and 12205, than apply into the LCM equation.

GCF(12200,12205) = 5
LCM(12200,12205) = ( 12200 × 12205) / 5
LCM(12200,12205) = 148901000 / 5
LCM(12200,12205) = 29780200

Properties of LCM 12200 and 12205

(i) The LCM of 12205 and 12200 is associative

LCM of 12200 and 12205 = LCM of 12205 and 12200

Related Least Common Multiples of 12200

Related Least Common Multiples of 12205

Frequently Asked Questions on LCM of 12200 and 12205

1. What is the LCM of 12200 and 12205?

Answer: LCM of 12200 and 12205 is 29780200.

2. What are the Factors of 12200?

Answer: Factors of 12200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 61, 100, 122, 200, 244, 305, 488, 610, 1220, 1525, 2440, 3050, 6100, 12200. There are 24 integers that are factors of 12200. The greatest factor of 12200 is 12200.

3. What are the Factors of 12205?

Answer: Factors of 12205 are 1, 5, 2441, 12205. There are 4 integers that are factors of 12205. The greatest factor of 12205 is 12205.

4. How to Find the LCM of 12200 and 12205?

Answer:

Least Common Multiple of 12200 and 12205 = 29780200

Step 1: Find the prime factorization of 12200

12200 = 2 x 2 x 2 x 5 x 5 x 61

Step 2: Find the prime factorization of 12205

12205 = 5 x 2441

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

LCM = 29780200 = 2 x 2 x 2 x 5 x 5 x 61 x 2441

Step 4: Therefore, the least common multiple of 12200 and 12205 is 29780200.