Least Common Multiple of 9750 and 9756

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9750 and 9756 the smallest integer that is 15853500 that is divisible by both numbers.

Least Common Multiple (LCM) of 9750 and 9756 is 15853500.

LCM(9750,9756) = 15853500

LCM of 9750 and 9756

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

LCM of:
and

Least Common Multiple of 9750 and 9756

LCM of 9750 and 9756 is 15853500

Least common multiple can be found by multiplying the highest exponent prime factors of 9750 and 9756. First we will calculate the prime factors of 9750 and 9756.

Prime Factorization of 9750


2 9750
3 4875
5 1625
5 325
5 65
13 13
1

Prime factors of 9750 are 2, 3, 5,13. Prime factorization of 9750 in exponential form is:

9750 = 21×31×53×131

Prime Factorization of 9756


2 9756
2 4878
3 2439
3 813
271 271
1

Prime factors of 9756 are 2, 3,271. Prime factorization of 9756 in exponential form is:

9756 = 22×32×2711

Now multiplying the highest exponent prime factors to calculate the LCM of 9750 and 9756.

LCM(9750,9756) = 22×32×53×131×2711
LCM(9750,9756) = 15853500

Factors of 9750

List of positive integer factors of 9750 that divides 9750 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 125, 130, 150, 195, 250, 325, 375, 390, 650, 750, 975, 1625, 1950, 3250, 4875, 9750

Factors of 9756

List of positive integer factors of 9756 that divides 9756 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 271, 542, 813, 1084, 1626, 2439, 3252, 4878, 9756

Least Common Multiple of 9750 and 9756 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9750 and 9756, than apply into the LCM equation.

GCF(9750,9756) = 6
LCM(9750,9756) = ( 9750 × 9756) / 6
LCM(9750,9756) = 95121000 / 6
LCM(9750,9756) = 15853500

Properties of LCM 9750 and 9756

(i) The LCM of 9756 and 9750 is associative

LCM of 9750 and 9756 = LCM of 9756 and 9750

Related Least Common Multiples of 9750

Related Least Common Multiples of 9756

Frequently Asked Questions on LCM of 9750 and 9756

1. What is the LCM of 9750 and 9756?

Answer: LCM of 9750 and 9756 is 15853500.

2. What are the Factors of 9750?

Answer: Factors of 9750 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 125, 130, 150, 195, 250, 325, 375, 390, 650, 750, 975, 1625, 1950, 3250, 4875, 9750. There are 32 integers that are factors of 9750. The greatest factor of 9750 is 9750.

3. What are the Factors of 9756?

Answer: Factors of 9756 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 271, 542, 813, 1084, 1626, 2439, 3252, 4878, 9756. There are 18 integers that are factors of 9756. The greatest factor of 9756 is 9756.

4. How to Find the LCM of 9750 and 9756?

Answer:

Least Common Multiple of 9750 and 9756 = 15853500

Step 1: Find the prime factorization of 9750

9750 = 2 x 3 x 5 x 5 x 5 x 13

Step 2: Find the prime factorization of 9756

9756 = 2 x 2 x 3 x 3 x 271

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

LCM = 15853500 = 2 x 2 x 3 x 3 x 5 x 5 x 5 x 13 x 271

Step 4: Therefore, the least common multiple of 9750 and 9756 is 15853500.