Least Common Multiple of 9760 and 9768

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9760 and 9768 the smallest integer that is 11916960 that is divisible by both numbers.

Least Common Multiple (LCM) of 9760 and 9768 is 11916960.

LCM(9760,9768) = 11916960

LCM of 9760 and 9768

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

LCM of:
and

Least Common Multiple of 9760 and 9768

LCM of 9760 and 9768 is 11916960

Least common multiple can be found by multiplying the highest exponent prime factors of 9760 and 9768. First we will calculate the prime factors of 9760 and 9768.

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

Prime Factorization of 9768


2 9768
2 4884
2 2442
3 1221
11 407
37 37
1

Prime factors of 9768 are 2, 3, 11,37. Prime factorization of 9768 in exponential form is:

9768 = 23×31×111×371

Now multiplying the highest exponent prime factors to calculate the LCM of 9760 and 9768.

LCM(9760,9768) = 25×31×51×111×371×611
LCM(9760,9768) = 11916960

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

Factors of 9768

List of positive integer factors of 9768 that divides 9768 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 37, 44, 66, 74, 88, 111, 132, 148, 222, 264, 296, 407, 444, 814, 888, 1221, 1628, 2442, 3256, 4884, 9768

Least Common Multiple of 9760 and 9768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9760 and 9768, than apply into the LCM equation.

GCF(9760,9768) = 8
LCM(9760,9768) = ( 9760 × 9768) / 8
LCM(9760,9768) = 95335680 / 8
LCM(9760,9768) = 11916960

Properties of LCM 9760 and 9768

(i) The LCM of 9768 and 9760 is associative

LCM of 9760 and 9768 = LCM of 9768 and 9760

Related Least Common Multiples of 9760

Related Least Common Multiples of 9768

Frequently Asked Questions on LCM of 9760 and 9768

1. What is the LCM of 9760 and 9768?

Answer: LCM of 9760 and 9768 is 11916960.

2. 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.

3. What are the Factors of 9768?

Answer: Factors of 9768 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 37, 44, 66, 74, 88, 111, 132, 148, 222, 264, 296, 407, 444, 814, 888, 1221, 1628, 2442, 3256, 4884, 9768. There are 32 integers that are factors of 9768. The greatest factor of 9768 is 9768.

4. How to Find the LCM of 9760 and 9768?

Answer:

Least Common Multiple of 9760 and 9768 = 11916960

Step 1: Find the prime factorization of 9760

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

Step 2: Find the prime factorization of 9768

9768 = 2 x 2 x 2 x 3 x 11 x 37

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

LCM = 11916960 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 11 x 37 x 61

Step 4: Therefore, the least common multiple of 9760 and 9768 is 11916960.