Least Common Multiple of 2400 and 2405

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2400 and 2405 the smallest integer that is 1154400 that is divisible by both numbers.

Least Common Multiple (LCM) of 2400 and 2405 is 1154400.

LCM(2400,2405) = 1154400

LCM of 2400 and 2405

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

LCM of:
and

Least Common Multiple of 2400 and 2405

LCM of 2400 and 2405 is 1154400

Least common multiple can be found by multiplying the highest exponent prime factors of 2400 and 2405. First we will calculate the prime factors of 2400 and 2405.

Prime Factorization of 2400


2 2400
2 1200
2 600
2 300
2 150
3 75
5 25
5 5
1

Prime factors of 2400 are 2, 3,5. Prime factorization of 2400 in exponential form is:

2400 = 25×31×52

Prime Factorization of 2405


5 2405
13 481
37 37
1

Prime factors of 2405 are 5, 13,37. Prime factorization of 2405 in exponential form is:

2405 = 51×131×371

Now multiplying the highest exponent prime factors to calculate the LCM of 2400 and 2405.

LCM(2400,2405) = 25×31×52×131×371
LCM(2400,2405) = 1154400

Factors of 2400

List of positive integer factors of 2400 that divides 2400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400

Factors of 2405

List of positive integer factors of 2405 that divides 2405 without a remainder.

1, 5, 13, 37, 65, 185, 481, 2405

Least Common Multiple of 2400 and 2405 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2400 and 2405, than apply into the LCM equation.

GCF(2400,2405) = 5
LCM(2400,2405) = ( 2400 × 2405) / 5
LCM(2400,2405) = 5772000 / 5
LCM(2400,2405) = 1154400

Properties of LCM 2400 and 2405

(i) The LCM of 2405 and 2400 is associative

LCM of 2400 and 2405 = LCM of 2405 and 2400

Related Least Common Multiples of 2400

Related Least Common Multiples of 2405

Frequently Asked Questions on LCM of 2400 and 2405

1. What is the LCM of 2400 and 2405?

Answer: LCM of 2400 and 2405 is 1154400.

2. What are the Factors of 2400?

Answer: Factors of 2400 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 150, 160, 200, 240, 300, 400, 480, 600, 800, 1200, 2400. There are 36 integers that are factors of 2400. The greatest factor of 2400 is 2400.

3. What are the Factors of 2405?

Answer: Factors of 2405 are 1, 5, 13, 37, 65, 185, 481, 2405. There are 8 integers that are factors of 2405. The greatest factor of 2405 is 2405.

4. How to Find the LCM of 2400 and 2405?

Answer:

Least Common Multiple of 2400 and 2405 = 1154400

Step 1: Find the prime factorization of 2400

2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5

Step 2: Find the prime factorization of 2405

2405 = 5 x 13 x 37

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

LCM = 1154400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 13 x 37

Step 4: Therefore, the least common multiple of 2400 and 2405 is 1154400.