Least Common Multiple of 9996 and 10000

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9996 and 10000 the smallest integer that is 24990000 that is divisible by both numbers.

Least Common Multiple (LCM) of 9996 and 10000 is 24990000.

LCM(9996,10000) = 24990000

LCM of 9996 and 10000

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

LCM of:
and

Least Common Multiple of 9996 and 10000

LCM of 9996 and 10000 is 24990000

Least common multiple can be found by multiplying the highest exponent prime factors of 9996 and 10000. First we will calculate the prime factors of 9996 and 10000.

Prime Factorization of 9996


2 9996
2 4998
3 2499
7 833
7 119
17 17
1

Prime factors of 9996 are 2, 3, 7,17. Prime factorization of 9996 in exponential form is:

9996 = 22×31×72×171

Prime Factorization of 10000


2 10000
2 5000
2 2500
2 1250
5 625
5 125
5 25
5 5
1

Prime factors of 10000 are 2,5. Prime factorization of 10000 in exponential form is:

10000 = 24×54

Now multiplying the highest exponent prime factors to calculate the LCM of 9996 and 10000.

LCM(9996,10000) = 24×31×54×72×171
LCM(9996,10000) = 24990000

Factors of 9996

List of positive integer factors of 9996 that divides 9996 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 49, 51, 68, 84, 98, 102, 119, 147, 196, 204, 238, 294, 357, 476, 588, 714, 833, 1428, 1666, 2499, 3332, 4998, 9996

Factors of 10000

List of positive integer factors of 10000 that divides 10000 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000

Least Common Multiple of 9996 and 10000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9996 and 10000, than apply into the LCM equation.

GCF(9996,10000) = 4
LCM(9996,10000) = ( 9996 × 10000) / 4
LCM(9996,10000) = 99960000 / 4
LCM(9996,10000) = 24990000

Properties of LCM 9996 and 10000

(i) The LCM of 10000 and 9996 is associative

LCM of 9996 and 10000 = LCM of 10000 and 9996

Related Least Common Multiples of 9996

Related Least Common Multiples of 10000

Frequently Asked Questions on LCM of 9996 and 10000

1. What is the LCM of 9996 and 10000?

Answer: LCM of 9996 and 10000 is 24990000.

2. What are the Factors of 9996?

Answer: Factors of 9996 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 49, 51, 68, 84, 98, 102, 119, 147, 196, 204, 238, 294, 357, 476, 588, 714, 833, 1428, 1666, 2499, 3332, 4998, 9996. There are 36 integers that are factors of 9996. The greatest factor of 9996 is 9996.

3. What are the Factors of 10000?

Answer: Factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, 10000. There are 25 integers that are factors of 10000. The greatest factor of 10000 is 10000.

4. How to Find the LCM of 9996 and 10000?

Answer:

Least Common Multiple of 9996 and 10000 = 24990000

Step 1: Find the prime factorization of 9996

9996 = 2 x 2 x 3 x 7 x 7 x 17

Step 2: Find the prime factorization of 10000

10000 = 2 x 2 x 2 x 2 x 5 x 5 x 5 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 = 24990000 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 5 x 7 x 7 x 17

Step 4: Therefore, the least common multiple of 9996 and 10000 is 24990000.