Least Common Multiple of 32000 and 32001

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 32000 and 32001 the smallest integer that is 1024032000 that is divisible by both numbers.

Least Common Multiple (LCM) of 32000 and 32001 is 1024032000.

LCM(32000,32001) = 1024032000

LCM of 32000 and 32001

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

LCM of:
and

Least Common Multiple of 32000 and 32001

LCM of 32000 and 32001 is 1024032000

Least common multiple can be found by multiplying the highest exponent prime factors of 32000 and 32001. First we will calculate the prime factors of 32000 and 32001.

Prime Factorization of 32000


2 32000
2 16000
2 8000
2 4000
2 2000
2 1000
2 500
2 250
5 125
5 25
5 5
1

Prime factors of 32000 are 2,5. Prime factorization of 32000 in exponential form is:

32000 = 28×53

Prime Factorization of 32001


3 32001
10667 10667
1

Prime factors of 32001 are 3,10667. Prime factorization of 32001 in exponential form is:

32001 = 31×106671

Now multiplying the highest exponent prime factors to calculate the LCM of 32000 and 32001.

LCM(32000,32001) = 28×31×53×106671
LCM(32000,32001) = 1024032000

Factors of 32000

List of positive integer factors of 32000 that divides 32000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 640, 800, 1000, 1280, 1600, 2000, 3200, 4000, 6400, 8000, 16000, 32000

Factors of 32001

List of positive integer factors of 32001 that divides 32001 without a remainder.

1, 3, 10667, 32001

Least Common Multiple of 32000 and 32001 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32000 and 32001, than apply into the LCM equation.

GCF(32000,32001) = 1
LCM(32000,32001) = ( 32000 × 32001) / 1
LCM(32000,32001) = 1024032000 / 1
LCM(32000,32001) = 1024032000

Properties of LCM 32000 and 32001

(i) The LCM of 32001 and 32000 is associative

LCM of 32000 and 32001 = LCM of 32001 and 32000

Related Least Common Multiples of 32000

Related Least Common Multiples of 32001

Frequently Asked Questions on LCM of 32000 and 32001

1. What is the LCM of 32000 and 32001?

Answer: LCM of 32000 and 32001 is 1024032000.

2. What are the Factors of 32000?

Answer: Factors of 32000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 640, 800, 1000, 1280, 1600, 2000, 3200, 4000, 6400, 8000, 16000, 32000. There are 36 integers that are factors of 32000. The greatest factor of 32000 is 32000.

3. What are the Factors of 32001?

Answer: Factors of 32001 are 1, 3, 10667, 32001. There are 4 integers that are factors of 32001. The greatest factor of 32001 is 32001.

4. How to Find the LCM of 32000 and 32001?

Answer:

Least Common Multiple of 32000 and 32001 = 1024032000

Step 1: Find the prime factorization of 32000

32000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5

Step 2: Find the prime factorization of 32001

32001 = 3 x 10667

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

LCM = 1024032000 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 10667

Step 4: Therefore, the least common multiple of 32000 and 32001 is 1024032000.