Least Common Multiple of 9675 and 9680

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9675 and 9680 the smallest integer that is 18730800 that is divisible by both numbers.

Least Common Multiple (LCM) of 9675 and 9680 is 18730800.

LCM(9675,9680) = 18730800

LCM of 9675 and 9680

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

LCM of:
and

Least Common Multiple of 9675 and 9680

LCM of 9675 and 9680 is 18730800

Least common multiple can be found by multiplying the highest exponent prime factors of 9675 and 9680. First we will calculate the prime factors of 9675 and 9680.

Prime Factorization of 9675


3 9675
3 3225
5 1075
5 215
43 43
1

Prime factors of 9675 are 3, 5,43. Prime factorization of 9675 in exponential form is:

9675 = 32×52×431

Prime Factorization of 9680


2 9680
2 4840
2 2420
2 1210
5 605
11 121
11 11
1

Prime factors of 9680 are 2, 5,11. Prime factorization of 9680 in exponential form is:

9680 = 24×51×112

Now multiplying the highest exponent prime factors to calculate the LCM of 9675 and 9680.

LCM(9675,9680) = 24×32×52×112×431
LCM(9675,9680) = 18730800

Factors of 9675

List of positive integer factors of 9675 that divides 9675 without a remainder.

1, 3, 5, 9, 15, 25, 43, 45, 75, 129, 215, 225, 387, 645, 1075, 1935, 3225, 9675

Factors of 9680

List of positive integer factors of 9680 that divides 9680 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 121, 176, 220, 242, 440, 484, 605, 880, 968, 1210, 1936, 2420, 4840, 9680

Least Common Multiple of 9675 and 9680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9675 and 9680, than apply into the LCM equation.

GCF(9675,9680) = 5
LCM(9675,9680) = ( 9675 × 9680) / 5
LCM(9675,9680) = 93654000 / 5
LCM(9675,9680) = 18730800

Properties of LCM 9675 and 9680

(i) The LCM of 9680 and 9675 is associative

LCM of 9675 and 9680 = LCM of 9680 and 9675

Related Least Common Multiples of 9675

Related Least Common Multiples of 9680

Frequently Asked Questions on LCM of 9675 and 9680

1. What is the LCM of 9675 and 9680?

Answer: LCM of 9675 and 9680 is 18730800.

2. What are the Factors of 9675?

Answer: Factors of 9675 are 1, 3, 5, 9, 15, 25, 43, 45, 75, 129, 215, 225, 387, 645, 1075, 1935, 3225, 9675. There are 18 integers that are factors of 9675. The greatest factor of 9675 is 9675.

3. What are the Factors of 9680?

Answer: Factors of 9680 are 1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 40, 44, 55, 80, 88, 110, 121, 176, 220, 242, 440, 484, 605, 880, 968, 1210, 1936, 2420, 4840, 9680. There are 30 integers that are factors of 9680. The greatest factor of 9680 is 9680.

4. How to Find the LCM of 9675 and 9680?

Answer:

Least Common Multiple of 9675 and 9680 = 18730800

Step 1: Find the prime factorization of 9675

9675 = 3 x 3 x 5 x 5 x 43

Step 2: Find the prime factorization of 9680

9680 = 2 x 2 x 2 x 2 x 5 x 11 x 11

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

LCM = 18730800 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 11 x 11 x 43

Step 4: Therefore, the least common multiple of 9675 and 9680 is 18730800.