Least Common Multiple of 2400 and 2407

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 2407 the smallest integer that is 5776800 that is divisible by both numbers.

Least Common Multiple (LCM) of 2400 and 2407 is 5776800.

LCM(2400,2407) = 5776800

LCM of 2400 and 2407

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

LCM of:
and

Least Common Multiple of 2400 and 2407

LCM of 2400 and 2407 is 5776800

Least common multiple can be found by multiplying the highest exponent prime factors of 2400 and 2407. First we will calculate the prime factors of 2400 and 2407.

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 2407


29 2407
83 83
1

Prime factors of 2407 are 29,83. Prime factorization of 2407 in exponential form is:

2407 = 291×831

Now multiplying the highest exponent prime factors to calculate the LCM of 2400 and 2407.

LCM(2400,2407) = 25×31×52×291×831
LCM(2400,2407) = 5776800

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 2407

List of positive integer factors of 2407 that divides 2407 without a remainder.

1, 29, 83, 2407

Least Common Multiple of 2400 and 2407 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 2407, than apply into the LCM equation.

GCF(2400,2407) = 1
LCM(2400,2407) = ( 2400 × 2407) / 1
LCM(2400,2407) = 5776800 / 1
LCM(2400,2407) = 5776800

Properties of LCM 2400 and 2407

(i) The LCM of 2407 and 2400 is associative

LCM of 2400 and 2407 = LCM of 2407 and 2400

Related Least Common Multiples of 2400

Related Least Common Multiples of 2407

Frequently Asked Questions on LCM of 2400 and 2407

1. What is the LCM of 2400 and 2407?

Answer: LCM of 2400 and 2407 is 5776800.

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 2407?

Answer: Factors of 2407 are 1, 29, 83, 2407. There are 4 integers that are factors of 2407. The greatest factor of 2407 is 2407.

4. How to Find the LCM of 2400 and 2407?

Answer:

Least Common Multiple of 2400 and 2407 = 5776800

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 2407

2407 = 29 x 83

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

LCM = 5776800 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 29 x 83

Step 4: Therefore, the least common multiple of 2400 and 2407 is 5776800.