Least Common Multiple of 9724 and 9729

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 9729 the smallest integer that is 94604796 that is divisible by both numbers.

Least Common Multiple (LCM) of 9724 and 9729 is 94604796.

LCM(9724,9729) = 94604796

LCM of 9724 and 9729

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

LCM of:
and

Least Common Multiple of 9724 and 9729

LCM of 9724 and 9729 is 94604796

Least common multiple can be found by multiplying the highest exponent prime factors of 9724 and 9729. First we will calculate the prime factors of 9724 and 9729.

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 9729


3 9729
3 3243
23 1081
47 47
1

Prime factors of 9729 are 3, 23,47. Prime factorization of 9729 in exponential form is:

9729 = 32×231×471

Now multiplying the highest exponent prime factors to calculate the LCM of 9724 and 9729.

LCM(9724,9729) = 22×32×111×131×171×231×471
LCM(9724,9729) = 94604796

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 9729

List of positive integer factors of 9729 that divides 9729 without a remainder.

1, 3, 9, 23, 47, 69, 141, 207, 423, 1081, 3243, 9729

Least Common Multiple of 9724 and 9729 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 9729, than apply into the LCM equation.

GCF(9724,9729) = 1
LCM(9724,9729) = ( 9724 × 9729) / 1
LCM(9724,9729) = 94604796 / 1
LCM(9724,9729) = 94604796

Properties of LCM 9724 and 9729

(i) The LCM of 9729 and 9724 is associative

LCM of 9724 and 9729 = LCM of 9729 and 9724

Related Least Common Multiples of 9724

Related Least Common Multiples of 9729

Frequently Asked Questions on LCM of 9724 and 9729

1. What is the LCM of 9724 and 9729?

Answer: LCM of 9724 and 9729 is 94604796.

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 9729?

Answer: Factors of 9729 are 1, 3, 9, 23, 47, 69, 141, 207, 423, 1081, 3243, 9729. There are 12 integers that are factors of 9729. The greatest factor of 9729 is 9729.

4. How to Find the LCM of 9724 and 9729?

Answer:

Least Common Multiple of 9724 and 9729 = 94604796

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 9729

9729 = 3 x 3 x 23 x 47

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

LCM = 94604796 = 2 x 2 x 3 x 3 x 11 x 13 x 17 x 23 x 47

Step 4: Therefore, the least common multiple of 9724 and 9729 is 94604796.