Least Common Multiple of 9594 and 9600

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9594 and 9600 the smallest integer that is 15350400 that is divisible by both numbers.

Least Common Multiple (LCM) of 9594 and 9600 is 15350400.

LCM(9594,9600) = 15350400

LCM of 9594 and 9600

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

LCM of:
and

Least Common Multiple of 9594 and 9600

LCM of 9594 and 9600 is 15350400

Least common multiple can be found by multiplying the highest exponent prime factors of 9594 and 9600. First we will calculate the prime factors of 9594 and 9600.

Prime Factorization of 9594


2 9594
3 4797
3 1599
13 533
41 41
1

Prime factors of 9594 are 2, 3, 13,41. Prime factorization of 9594 in exponential form is:

9594 = 21×32×131×411

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

Now multiplying the highest exponent prime factors to calculate the LCM of 9594 and 9600.

LCM(9594,9600) = 27×32×52×131×411
LCM(9594,9600) = 15350400

Factors of 9594

List of positive integer factors of 9594 that divides 9594 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 41, 78, 82, 117, 123, 234, 246, 369, 533, 738, 1066, 1599, 3198, 4797, 9594

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

Least Common Multiple of 9594 and 9600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9594 and 9600, than apply into the LCM equation.

GCF(9594,9600) = 6
LCM(9594,9600) = ( 9594 × 9600) / 6
LCM(9594,9600) = 92102400 / 6
LCM(9594,9600) = 15350400

Properties of LCM 9594 and 9600

(i) The LCM of 9600 and 9594 is associative

LCM of 9594 and 9600 = LCM of 9600 and 9594

Related Least Common Multiples of 9594

Related Least Common Multiples of 9600

Frequently Asked Questions on LCM of 9594 and 9600

1. What is the LCM of 9594 and 9600?

Answer: LCM of 9594 and 9600 is 15350400.

2. What are the Factors of 9594?

Answer: Factors of 9594 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 41, 78, 82, 117, 123, 234, 246, 369, 533, 738, 1066, 1599, 3198, 4797, 9594. There are 24 integers that are factors of 9594. The greatest factor of 9594 is 9594.

3. 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.

4. How to Find the LCM of 9594 and 9600?

Answer:

Least Common Multiple of 9594 and 9600 = 15350400

Step 1: Find the prime factorization of 9594

9594 = 2 x 3 x 3 x 13 x 41

Step 2: 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 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 15350400 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 13 x 41

Step 4: Therefore, the least common multiple of 9594 and 9600 is 15350400.