Least Common Multiple of 9600 and 9604

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9600 and 9604 the smallest integer that is 23049600 that is divisible by both numbers.

Least Common Multiple (LCM) of 9600 and 9604 is 23049600.

LCM(9600,9604) = 23049600

LCM of 9600 and 9604

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

LCM of:
and

Least Common Multiple of 9600 and 9604

LCM of 9600 and 9604 is 23049600

Least common multiple can be found by multiplying the highest exponent prime factors of 9600 and 9604. First we will calculate the prime factors of 9600 and 9604.

Prime Factorization of 9600


2 9600
2 4800
2 2400
2 1200
2 600
2 300
2 150
3 75
5 25
5 5
1

Prime factors of 9600 are 2, 3,5. Prime factorization of 9600 in exponential form is:

9600 = 27×31×52

Prime Factorization of 9604


2 9604
2 4802
7 2401
7 343
7 49
7 7
1

Prime factors of 9604 are 2,7. Prime factorization of 9604 in exponential form is:

9604 = 22×74

Now multiplying the highest exponent prime factors to calculate the LCM of 9600 and 9604.

LCM(9600,9604) = 27×31×52×74
LCM(9600,9604) = 23049600

Factors of 9600

List of positive integer factors of 9600 that divides 9600 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600

Factors of 9604

List of positive integer factors of 9604 that divides 9604 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, 9604

Least Common Multiple of 9600 and 9604 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9600 and 9604, than apply into the LCM equation.

GCF(9600,9604) = 4
LCM(9600,9604) = ( 9600 × 9604) / 4
LCM(9600,9604) = 92198400 / 4
LCM(9600,9604) = 23049600

Properties of LCM 9600 and 9604

(i) The LCM of 9604 and 9600 is associative

LCM of 9600 and 9604 = LCM of 9604 and 9600

Related Least Common Multiples of 9600

Related Least Common Multiples of 9604

Frequently Asked Questions on LCM of 9600 and 9604

1. What is the LCM of 9600 and 9604?

Answer: LCM of 9600 and 9604 is 23049600.

2. What are the Factors of 9600?

Answer: Factors of 9600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 300, 320, 384, 400, 480, 600, 640, 800, 960, 1200, 1600, 1920, 2400, 3200, 4800, 9600. There are 48 integers that are factors of 9600. The greatest factor of 9600 is 9600.

3. What are the Factors of 9604?

Answer: Factors of 9604 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372, 2401, 4802, 9604. There are 15 integers that are factors of 9604. The greatest factor of 9604 is 9604.

4. How to Find the LCM of 9600 and 9604?

Answer:

Least Common Multiple of 9600 and 9604 = 23049600

Step 1: Find the prime factorization of 9600

9600 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5

Step 2: Find the prime factorization of 9604

9604 = 2 x 2 x 7 x 7 x 7 x 7

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

LCM = 23049600 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 7 x 7 x 7

Step 4: Therefore, the least common multiple of 9600 and 9604 is 23049600.