Least Common Multiple of 9894 and 9900

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9894 and 9900 the smallest integer that is 16325100 that is divisible by both numbers.

Least Common Multiple (LCM) of 9894 and 9900 is 16325100.

LCM(9894,9900) = 16325100

LCM of 9894 and 9900

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

LCM of:
and

Least Common Multiple of 9894 and 9900

LCM of 9894 and 9900 is 16325100

Least common multiple can be found by multiplying the highest exponent prime factors of 9894 and 9900. First we will calculate the prime factors of 9894 and 9900.

Prime Factorization of 9894


2 9894
3 4947
17 1649
97 97
1

Prime factors of 9894 are 2, 3, 17,97. Prime factorization of 9894 in exponential form is:

9894 = 21×31×171×971

Prime Factorization of 9900


2 9900
2 4950
3 2475
3 825
5 275
5 55
11 11
1

Prime factors of 9900 are 2, 3, 5,11. Prime factorization of 9900 in exponential form is:

9900 = 22×32×52×111

Now multiplying the highest exponent prime factors to calculate the LCM of 9894 and 9900.

LCM(9894,9900) = 22×32×52×111×171×971
LCM(9894,9900) = 16325100

Factors of 9894

List of positive integer factors of 9894 that divides 9894 without a remainder.

1, 2, 3, 6, 17, 34, 51, 97, 102, 194, 291, 582, 1649, 3298, 4947, 9894

Factors of 9900

List of positive integer factors of 9900 that divides 9900 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950, 9900

Least Common Multiple of 9894 and 9900 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9894 and 9900, than apply into the LCM equation.

GCF(9894,9900) = 6
LCM(9894,9900) = ( 9894 × 9900) / 6
LCM(9894,9900) = 97950600 / 6
LCM(9894,9900) = 16325100

Properties of LCM 9894 and 9900

(i) The LCM of 9900 and 9894 is associative

LCM of 9894 and 9900 = LCM of 9900 and 9894

Related Least Common Multiples of 9894

Related Least Common Multiples of 9900

Frequently Asked Questions on LCM of 9894 and 9900

1. What is the LCM of 9894 and 9900?

Answer: LCM of 9894 and 9900 is 16325100.

2. What are the Factors of 9894?

Answer: Factors of 9894 are 1, 2, 3, 6, 17, 34, 51, 97, 102, 194, 291, 582, 1649, 3298, 4947, 9894. There are 16 integers that are factors of 9894. The greatest factor of 9894 is 9894.

3. What are the Factors of 9900?

Answer: Factors of 9900 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 132, 150, 165, 180, 198, 220, 225, 275, 300, 330, 396, 450, 495, 550, 660, 825, 900, 990, 1100, 1650, 1980, 2475, 3300, 4950, 9900. There are 54 integers that are factors of 9900. The greatest factor of 9900 is 9900.

4. How to Find the LCM of 9894 and 9900?

Answer:

Least Common Multiple of 9894 and 9900 = 16325100

Step 1: Find the prime factorization of 9894

9894 = 2 x 3 x 17 x 97

Step 2: Find the prime factorization of 9900

9900 = 2 x 2 x 3 x 3 x 5 x 5 x 11

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

LCM = 16325100 = 2 x 2 x 3 x 3 x 5 x 5 x 11 x 17 x 97

Step 4: Therefore, the least common multiple of 9894 and 9900 is 16325100.