Least Common Multiple of 9597 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 9597 and 9600 the smallest integer that is 30710400 that is divisible by both numbers.

Least Common Multiple (LCM) of 9597 and 9600 is 30710400.

LCM(9597,9600) = 30710400

LCM of 9597 and 9600

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

LCM of:
and

Least Common Multiple of 9597 and 9600

LCM of 9597 and 9600 is 30710400

Least common multiple can be found by multiplying the highest exponent prime factors of 9597 and 9600. First we will calculate the prime factors of 9597 and 9600.

Prime Factorization of 9597


3 9597
7 3199
457 457
1

Prime factors of 9597 are 3, 7,457. Prime factorization of 9597 in exponential form is:

9597 = 31×71×4571

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 9597 and 9600.

LCM(9597,9600) = 27×31×52×71×4571
LCM(9597,9600) = 30710400

Factors of 9597

List of positive integer factors of 9597 that divides 9597 without a remainder.

1, 3, 7, 21, 457, 1371, 3199, 9597

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 9597 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 9597 and 9600, than apply into the LCM equation.

GCF(9597,9600) = 3
LCM(9597,9600) = ( 9597 × 9600) / 3
LCM(9597,9600) = 92131200 / 3
LCM(9597,9600) = 30710400

Properties of LCM 9597 and 9600

(i) The LCM of 9600 and 9597 is associative

LCM of 9597 and 9600 = LCM of 9600 and 9597

Related Least Common Multiples of 9597

Related Least Common Multiples of 9600

Frequently Asked Questions on LCM of 9597 and 9600

1. What is the LCM of 9597 and 9600?

Answer: LCM of 9597 and 9600 is 30710400.

2. What are the Factors of 9597?

Answer: Factors of 9597 are 1, 3, 7, 21, 457, 1371, 3199, 9597. There are 8 integers that are factors of 9597. The greatest factor of 9597 is 9597.

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 9597 and 9600?

Answer:

Least Common Multiple of 9597 and 9600 = 30710400

Step 1: Find the prime factorization of 9597

9597 = 3 x 7 x 457

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 = 30710400 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 457

Step 4: Therefore, the least common multiple of 9597 and 9600 is 30710400.