Least Common Multiple of 9760 and 9765

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 9765 the smallest integer that is 19061280 that is divisible by both numbers.

Least Common Multiple (LCM) of 9760 and 9765 is 19061280.

LCM(9760,9765) = 19061280

LCM of 9760 and 9765

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

LCM of:
and

Least Common Multiple of 9760 and 9765

LCM of 9760 and 9765 is 19061280

Least common multiple can be found by multiplying the highest exponent prime factors of 9760 and 9765. First we will calculate the prime factors of 9760 and 9765.

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 9765


3 9765
3 3255
5 1085
7 217
31 31
1

Prime factors of 9765 are 3, 5, 7,31. Prime factorization of 9765 in exponential form is:

9765 = 32×51×71×311

Now multiplying the highest exponent prime factors to calculate the LCM of 9760 and 9765.

LCM(9760,9765) = 25×32×51×71×311×611
LCM(9760,9765) = 19061280

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 9765

List of positive integer factors of 9765 that divides 9765 without a remainder.

1, 3, 5, 7, 9, 15, 21, 31, 35, 45, 63, 93, 105, 155, 217, 279, 315, 465, 651, 1085, 1395, 1953, 3255, 9765

Least Common Multiple of 9760 and 9765 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 9765, than apply into the LCM equation.

GCF(9760,9765) = 5
LCM(9760,9765) = ( 9760 × 9765) / 5
LCM(9760,9765) = 95306400 / 5
LCM(9760,9765) = 19061280

Properties of LCM 9760 and 9765

(i) The LCM of 9765 and 9760 is associative

LCM of 9760 and 9765 = LCM of 9765 and 9760

Related Least Common Multiples of 9760

Related Least Common Multiples of 9765

Frequently Asked Questions on LCM of 9760 and 9765

1. What is the LCM of 9760 and 9765?

Answer: LCM of 9760 and 9765 is 19061280.

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 9765?

Answer: Factors of 9765 are 1, 3, 5, 7, 9, 15, 21, 31, 35, 45, 63, 93, 105, 155, 217, 279, 315, 465, 651, 1085, 1395, 1953, 3255, 9765. There are 24 integers that are factors of 9765. The greatest factor of 9765 is 9765.

4. How to Find the LCM of 9760 and 9765?

Answer:

Least Common Multiple of 9760 and 9765 = 19061280

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 9765

9765 = 3 x 3 x 5 x 7 x 31

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

LCM = 19061280 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 x 31 x 61

Step 4: Therefore, the least common multiple of 9760 and 9765 is 19061280.