Least Common Multiple of 9723 and 9728

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9723 and 9728 the smallest integer that is 94585344 that is divisible by both numbers.

Least Common Multiple (LCM) of 9723 and 9728 is 94585344.

LCM(9723,9728) = 94585344

LCM of 9723 and 9728

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

LCM of:
and

Least Common Multiple of 9723 and 9728

LCM of 9723 and 9728 is 94585344

Least common multiple can be found by multiplying the highest exponent prime factors of 9723 and 9728. First we will calculate the prime factors of 9723 and 9728.

Prime Factorization of 9723


3 9723
7 3241
463 463
1

Prime factors of 9723 are 3, 7,463. Prime factorization of 9723 in exponential form is:

9723 = 31×71×4631

Prime Factorization of 9728


2 9728
2 4864
2 2432
2 1216
2 608
2 304
2 152
2 76
2 38
19 19
1

Prime factors of 9728 are 2,19. Prime factorization of 9728 in exponential form is:

9728 = 29×191

Now multiplying the highest exponent prime factors to calculate the LCM of 9723 and 9728.

LCM(9723,9728) = 29×31×71×191×4631
LCM(9723,9728) = 94585344

Factors of 9723

List of positive integer factors of 9723 that divides 9723 without a remainder.

1, 3, 7, 21, 463, 1389, 3241, 9723

Factors of 9728

List of positive integer factors of 9728 that divides 9728 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1216, 2432, 4864, 9728

Least Common Multiple of 9723 and 9728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9723 and 9728, than apply into the LCM equation.

GCF(9723,9728) = 1
LCM(9723,9728) = ( 9723 × 9728) / 1
LCM(9723,9728) = 94585344 / 1
LCM(9723,9728) = 94585344

Properties of LCM 9723 and 9728

(i) The LCM of 9728 and 9723 is associative

LCM of 9723 and 9728 = LCM of 9728 and 9723

Related Least Common Multiples of 9723

Related Least Common Multiples of 9728

Frequently Asked Questions on LCM of 9723 and 9728

1. What is the LCM of 9723 and 9728?

Answer: LCM of 9723 and 9728 is 94585344.

2. What are the Factors of 9723?

Answer: Factors of 9723 are 1, 3, 7, 21, 463, 1389, 3241, 9723. There are 8 integers that are factors of 9723. The greatest factor of 9723 is 9723.

3. What are the Factors of 9728?

Answer: Factors of 9728 are 1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1216, 2432, 4864, 9728. There are 20 integers that are factors of 9728. The greatest factor of 9728 is 9728.

4. How to Find the LCM of 9723 and 9728?

Answer:

Least Common Multiple of 9723 and 9728 = 94585344

Step 1: Find the prime factorization of 9723

9723 = 3 x 7 x 463

Step 2: Find the prime factorization of 9728

9728 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 19

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

LCM = 94585344 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 19 x 463

Step 4: Therefore, the least common multiple of 9723 and 9728 is 94585344.