Least Common Multiple of 2400 and 2408

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 2408 the smallest integer that is 722400 that is divisible by both numbers.

Least Common Multiple (LCM) of 2400 and 2408 is 722400.

LCM(2400,2408) = 722400

LCM of 2400 and 2408

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

LCM of:
and

Least Common Multiple of 2400 and 2408

LCM of 2400 and 2408 is 722400

Least common multiple can be found by multiplying the highest exponent prime factors of 2400 and 2408. First we will calculate the prime factors of 2400 and 2408.

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 2408


2 2408
2 1204
2 602
7 301
43 43
1

Prime factors of 2408 are 2, 7,43. Prime factorization of 2408 in exponential form is:

2408 = 23×71×431

Now multiplying the highest exponent prime factors to calculate the LCM of 2400 and 2408.

LCM(2400,2408) = 25×31×52×71×431
LCM(2400,2408) = 722400

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 2408

List of positive integer factors of 2408 that divides 2408 without a remainder.

1, 2, 4, 7, 8, 14, 28, 43, 56, 86, 172, 301, 344, 602, 1204, 2408

Least Common Multiple of 2400 and 2408 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 2408, than apply into the LCM equation.

GCF(2400,2408) = 8
LCM(2400,2408) = ( 2400 × 2408) / 8
LCM(2400,2408) = 5779200 / 8
LCM(2400,2408) = 722400

Properties of LCM 2400 and 2408

(i) The LCM of 2408 and 2400 is associative

LCM of 2400 and 2408 = LCM of 2408 and 2400

Related Least Common Multiples of 2400

Related Least Common Multiples of 2408

Frequently Asked Questions on LCM of 2400 and 2408

1. What is the LCM of 2400 and 2408?

Answer: LCM of 2400 and 2408 is 722400.

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 2408?

Answer: Factors of 2408 are 1, 2, 4, 7, 8, 14, 28, 43, 56, 86, 172, 301, 344, 602, 1204, 2408. There are 16 integers that are factors of 2408. The greatest factor of 2408 is 2408.

4. How to Find the LCM of 2400 and 2408?

Answer:

Least Common Multiple of 2400 and 2408 = 722400

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 2408

2408 = 2 x 2 x 2 x 7 x 43

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

LCM = 722400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 43

Step 4: Therefore, the least common multiple of 2400 and 2408 is 722400.