Least Common Multiple of 9724 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 9724 and 9728 the smallest integer that is 23648768 that is divisible by both numbers.

Least Common Multiple (LCM) of 9724 and 9728 is 23648768.

LCM(9724,9728) = 23648768

LCM of 9724 and 9728

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

LCM of:
and

Least Common Multiple of 9724 and 9728

LCM of 9724 and 9728 is 23648768

Least common multiple can be found by multiplying the highest exponent prime factors of 9724 and 9728. First we will calculate the prime factors of 9724 and 9728.

Prime Factorization of 9724


2 9724
2 4862
11 2431
13 221
17 17
1

Prime factors of 9724 are 2, 11, 13,17. Prime factorization of 9724 in exponential form is:

9724 = 22×111×131×171

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 9724 and 9728.

LCM(9724,9728) = 29×111×131×171×191
LCM(9724,9728) = 23648768

Factors of 9724

List of positive integer factors of 9724 that divides 9724 without a remainder.

1, 2, 4, 11, 13, 17, 22, 26, 34, 44, 52, 68, 143, 187, 221, 286, 374, 442, 572, 748, 884, 2431, 4862, 9724

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 9724 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 9724 and 9728, than apply into the LCM equation.

GCF(9724,9728) = 4
LCM(9724,9728) = ( 9724 × 9728) / 4
LCM(9724,9728) = 94595072 / 4
LCM(9724,9728) = 23648768

Properties of LCM 9724 and 9728

(i) The LCM of 9728 and 9724 is associative

LCM of 9724 and 9728 = LCM of 9728 and 9724

Related Least Common Multiples of 9724

Related Least Common Multiples of 9728

Frequently Asked Questions on LCM of 9724 and 9728

1. What is the LCM of 9724 and 9728?

Answer: LCM of 9724 and 9728 is 23648768.

2. What are the Factors of 9724?

Answer: Factors of 9724 are 1, 2, 4, 11, 13, 17, 22, 26, 34, 44, 52, 68, 143, 187, 221, 286, 374, 442, 572, 748, 884, 2431, 4862, 9724. There are 24 integers that are factors of 9724. The greatest factor of 9724 is 9724.

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 9724 and 9728?

Answer:

Least Common Multiple of 9724 and 9728 = 23648768

Step 1: Find the prime factorization of 9724

9724 = 2 x 2 x 11 x 13 x 17

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 = 23648768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11 x 13 x 17 x 19

Step 4: Therefore, the least common multiple of 9724 and 9728 is 23648768.