Least Common Multiple of 9728 and 9732

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9728 and 9732 the smallest integer that is 23668224 that is divisible by both numbers.

Least Common Multiple (LCM) of 9728 and 9732 is 23668224.

LCM(9728,9732) = 23668224

LCM of 9728 and 9732

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

LCM of:
and

Least Common Multiple of 9728 and 9732

LCM of 9728 and 9732 is 23668224

Least common multiple can be found by multiplying the highest exponent prime factors of 9728 and 9732. First we will calculate the prime factors of 9728 and 9732.

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

Prime Factorization of 9732


2 9732
2 4866
3 2433
811 811
1

Prime factors of 9732 are 2, 3,811. Prime factorization of 9732 in exponential form is:

9732 = 22×31×8111

Now multiplying the highest exponent prime factors to calculate the LCM of 9728 and 9732.

LCM(9728,9732) = 29×31×191×8111
LCM(9728,9732) = 23668224

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

Factors of 9732

List of positive integer factors of 9732 that divides 9732 without a remainder.

1, 2, 3, 4, 6, 12, 811, 1622, 2433, 3244, 4866, 9732

Least Common Multiple of 9728 and 9732 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9728 and 9732, than apply into the LCM equation.

GCF(9728,9732) = 4
LCM(9728,9732) = ( 9728 × 9732) / 4
LCM(9728,9732) = 94672896 / 4
LCM(9728,9732) = 23668224

Properties of LCM 9728 and 9732

(i) The LCM of 9732 and 9728 is associative

LCM of 9728 and 9732 = LCM of 9732 and 9728

Related Least Common Multiples of 9728

Related Least Common Multiples of 9732

Frequently Asked Questions on LCM of 9728 and 9732

1. What is the LCM of 9728 and 9732?

Answer: LCM of 9728 and 9732 is 23668224.

2. 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.

3. What are the Factors of 9732?

Answer: Factors of 9732 are 1, 2, 3, 4, 6, 12, 811, 1622, 2433, 3244, 4866, 9732. There are 12 integers that are factors of 9732. The greatest factor of 9732 is 9732.

4. How to Find the LCM of 9728 and 9732?

Answer:

Least Common Multiple of 9728 and 9732 = 23668224

Step 1: 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 2: Find the prime factorization of 9732

9732 = 2 x 2 x 3 x 811

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

LCM = 23668224 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 19 x 811

Step 4: Therefore, the least common multiple of 9728 and 9732 is 23668224.