Least Common Multiple of 9730 and 9735

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9730 and 9735 the smallest integer that is 18944310 that is divisible by both numbers.

Least Common Multiple (LCM) of 9730 and 9735 is 18944310.

LCM(9730,9735) = 18944310

LCM of 9730 and 9735

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

LCM of:
and

Least Common Multiple of 9730 and 9735

LCM of 9730 and 9735 is 18944310

Least common multiple can be found by multiplying the highest exponent prime factors of 9730 and 9735. First we will calculate the prime factors of 9730 and 9735.

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

Prime Factorization of 9735


3 9735
5 3245
11 649
59 59
1

Prime factors of 9735 are 3, 5, 11,59. Prime factorization of 9735 in exponential form is:

9735 = 31×51×111×591

Now multiplying the highest exponent prime factors to calculate the LCM of 9730 and 9735.

LCM(9730,9735) = 21×31×51×71×111×591×1391
LCM(9730,9735) = 18944310

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

Factors of 9735

List of positive integer factors of 9735 that divides 9735 without a remainder.

1, 3, 5, 11, 15, 33, 55, 59, 165, 177, 295, 649, 885, 1947, 3245, 9735

Least Common Multiple of 9730 and 9735 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9730 and 9735, than apply into the LCM equation.

GCF(9730,9735) = 5
LCM(9730,9735) = ( 9730 × 9735) / 5
LCM(9730,9735) = 94721550 / 5
LCM(9730,9735) = 18944310

Properties of LCM 9730 and 9735

(i) The LCM of 9735 and 9730 is associative

LCM of 9730 and 9735 = LCM of 9735 and 9730

Related Least Common Multiples of 9730

Related Least Common Multiples of 9735

Frequently Asked Questions on LCM of 9730 and 9735

1. What is the LCM of 9730 and 9735?

Answer: LCM of 9730 and 9735 is 18944310.

2. 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.

3. What are the Factors of 9735?

Answer: Factors of 9735 are 1, 3, 5, 11, 15, 33, 55, 59, 165, 177, 295, 649, 885, 1947, 3245, 9735. There are 16 integers that are factors of 9735. The greatest factor of 9735 is 9735.

4. How to Find the LCM of 9730 and 9735?

Answer:

Least Common Multiple of 9730 and 9735 = 18944310

Step 1: Find the prime factorization of 9730

9730 = 2 x 5 x 7 x 139

Step 2: Find the prime factorization of 9735

9735 = 3 x 5 x 11 x 59

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

LCM = 18944310 = 2 x 3 x 5 x 7 x 11 x 59 x 139

Step 4: Therefore, the least common multiple of 9730 and 9735 is 18944310.