Least Common Multiple of 9756 and 9760

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9756 and 9760 the smallest integer that is 23804640 that is divisible by both numbers.

Least Common Multiple (LCM) of 9756 and 9760 is 23804640.

LCM(9756,9760) = 23804640

LCM of 9756 and 9760

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

LCM of:
and

Least Common Multiple of 9756 and 9760

LCM of 9756 and 9760 is 23804640

Least common multiple can be found by multiplying the highest exponent prime factors of 9756 and 9760. First we will calculate the prime factors of 9756 and 9760.

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

Prime Factorization of 9760


2 9760
2 4880
2 2440
2 1220
2 610
5 305
61 61
1

Prime factors of 9760 are 2, 5,61. Prime factorization of 9760 in exponential form is:

9760 = 25×51×611

Now multiplying the highest exponent prime factors to calculate the LCM of 9756 and 9760.

LCM(9756,9760) = 25×32×51×611×2711
LCM(9756,9760) = 23804640

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

Factors of 9760

List of positive integer factors of 9760 that divides 9760 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 61, 80, 122, 160, 244, 305, 488, 610, 976, 1220, 1952, 2440, 4880, 9760

Least Common Multiple of 9756 and 9760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9756 and 9760, than apply into the LCM equation.

GCF(9756,9760) = 4
LCM(9756,9760) = ( 9756 × 9760) / 4
LCM(9756,9760) = 95218560 / 4
LCM(9756,9760) = 23804640

Properties of LCM 9756 and 9760

(i) The LCM of 9760 and 9756 is associative

LCM of 9756 and 9760 = LCM of 9760 and 9756

Related Least Common Multiples of 9756

Related Least Common Multiples of 9760

Frequently Asked Questions on LCM of 9756 and 9760

1. What is the LCM of 9756 and 9760?

Answer: LCM of 9756 and 9760 is 23804640.

2. 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.

3. What are the Factors of 9760?

Answer: Factors of 9760 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 61, 80, 122, 160, 244, 305, 488, 610, 976, 1220, 1952, 2440, 4880, 9760. There are 24 integers that are factors of 9760. The greatest factor of 9760 is 9760.

4. How to Find the LCM of 9756 and 9760?

Answer:

Least Common Multiple of 9756 and 9760 = 23804640

Step 1: Find the prime factorization of 9756

9756 = 2 x 2 x 3 x 3 x 271

Step 2: Find the prime factorization of 9760

9760 = 2 x 2 x 2 x 2 x 2 x 5 x 61

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

LCM = 23804640 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 61 x 271

Step 4: Therefore, the least common multiple of 9756 and 9760 is 23804640.