Least Common Multiple of 10232 and 10240

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10232 and 10240 the smallest integer that is 13096960 that is divisible by both numbers.

Least Common Multiple (LCM) of 10232 and 10240 is 13096960.

LCM(10232,10240) = 13096960

LCM of 10232 and 10240

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

LCM of:
and

Least Common Multiple of 10232 and 10240

LCM of 10232 and 10240 is 13096960

Least common multiple can be found by multiplying the highest exponent prime factors of 10232 and 10240. First we will calculate the prime factors of 10232 and 10240.

Prime Factorization of 10232


2 10232
2 5116
2 2558
1279 1279
1

Prime factors of 10232 are 2,1279. Prime factorization of 10232 in exponential form is:

10232 = 23×12791

Prime Factorization of 10240


2 10240
2 5120
2 2560
2 1280
2 640
2 320
2 160
2 80
2 40
2 20
2 10
5 5
1

Prime factors of 10240 are 2,5. Prime factorization of 10240 in exponential form is:

10240 = 211×51

Now multiplying the highest exponent prime factors to calculate the LCM of 10232 and 10240.

LCM(10232,10240) = 211×51×12791
LCM(10232,10240) = 13096960

Factors of 10232

List of positive integer factors of 10232 that divides 10232 without a remainder.

1, 2, 4, 8, 1279, 2558, 5116, 10232

Factors of 10240

List of positive integer factors of 10240 that divides 10240 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 5120, 10240

Least Common Multiple of 10232 and 10240 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10232 and 10240, than apply into the LCM equation.

GCF(10232,10240) = 8
LCM(10232,10240) = ( 10232 × 10240) / 8
LCM(10232,10240) = 104775680 / 8
LCM(10232,10240) = 13096960

Properties of LCM 10232 and 10240

(i) The LCM of 10240 and 10232 is associative

LCM of 10232 and 10240 = LCM of 10240 and 10232

Related Least Common Multiples of 10232

Related Least Common Multiples of 10240

Frequently Asked Questions on LCM of 10232 and 10240

1. What is the LCM of 10232 and 10240?

Answer: LCM of 10232 and 10240 is 13096960.

2. What are the Factors of 10232?

Answer: Factors of 10232 are 1, 2, 4, 8, 1279, 2558, 5116, 10232. There are 8 integers that are factors of 10232. The greatest factor of 10232 is 10232.

3. What are the Factors of 10240?

Answer: Factors of 10240 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, 256, 320, 512, 640, 1024, 1280, 2048, 2560, 5120, 10240. There are 24 integers that are factors of 10240. The greatest factor of 10240 is 10240.

4. How to Find the LCM of 10232 and 10240?

Answer:

Least Common Multiple of 10232 and 10240 = 13096960

Step 1: Find the prime factorization of 10232

10232 = 2 x 2 x 2 x 1279

Step 2: Find the prime factorization of 10240

10240 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5

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

LCM = 13096960 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 1279

Step 4: Therefore, the least common multiple of 10232 and 10240 is 13096960.