Least Common Multiple of 9724 and 9730

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 9730 the smallest integer that is 47307260 that is divisible by both numbers.

Least Common Multiple (LCM) of 9724 and 9730 is 47307260.

LCM(9724,9730) = 47307260

LCM of 9724 and 9730

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

LCM of:
and

Least Common Multiple of 9724 and 9730

LCM of 9724 and 9730 is 47307260

Least common multiple can be found by multiplying the highest exponent prime factors of 9724 and 9730. First we will calculate the prime factors of 9724 and 9730.

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 9730


2 9730
5 4865
7 973
139 139
1

Prime factors of 9730 are 2, 5, 7,139. Prime factorization of 9730 in exponential form is:

9730 = 21×51×71×1391

Now multiplying the highest exponent prime factors to calculate the LCM of 9724 and 9730.

LCM(9724,9730) = 22×51×71×111×131×171×1391
LCM(9724,9730) = 47307260

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 9730

List of positive integer factors of 9730 that divides 9730 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 139, 278, 695, 973, 1390, 1946, 4865, 9730

Least Common Multiple of 9724 and 9730 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 9730, than apply into the LCM equation.

GCF(9724,9730) = 2
LCM(9724,9730) = ( 9724 × 9730) / 2
LCM(9724,9730) = 94614520 / 2
LCM(9724,9730) = 47307260

Properties of LCM 9724 and 9730

(i) The LCM of 9730 and 9724 is associative

LCM of 9724 and 9730 = LCM of 9730 and 9724

Related Least Common Multiples of 9724

Related Least Common Multiples of 9730

Frequently Asked Questions on LCM of 9724 and 9730

1. What is the LCM of 9724 and 9730?

Answer: LCM of 9724 and 9730 is 47307260.

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 9730?

Answer: Factors of 9730 are 1, 2, 5, 7, 10, 14, 35, 70, 139, 278, 695, 973, 1390, 1946, 4865, 9730. There are 16 integers that are factors of 9730. The greatest factor of 9730 is 9730.

4. How to Find the LCM of 9724 and 9730?

Answer:

Least Common Multiple of 9724 and 9730 = 47307260

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 9730

9730 = 2 x 5 x 7 x 139

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

LCM = 47307260 = 2 x 2 x 5 x 7 x 11 x 13 x 17 x 139

Step 4: Therefore, the least common multiple of 9724 and 9730 is 47307260.