Least Common Multiple of 2099 and 2100

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2099 and 2100 the smallest integer that is 4407900 that is divisible by both numbers.

Least Common Multiple (LCM) of 2099 and 2100 is 4407900.

LCM(2099,2100) = 4407900

LCM of 2099 and 2100

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

LCM of:
and

Least Common Multiple of 2099 and 2100

LCM of 2099 and 2100 is 4407900

Least common multiple can be found by multiplying the highest exponent prime factors of 2099 and 2100. First we will calculate the prime factors of 2099 and 2100.

Prime Factorization of 2099


2099 2099
1

Prime factors of 2099 are 2099. Prime factorization of 2099 in exponential form is:

2099 = 20991

Prime Factorization of 2100


2 2100
2 1050
3 525
5 175
5 35
7 7
1

Prime factors of 2100 are 2, 3, 5,7. Prime factorization of 2100 in exponential form is:

2100 = 22×31×52×71

Now multiplying the highest exponent prime factors to calculate the LCM of 2099 and 2100.

LCM(2099,2100) = 22×31×52×71×20991
LCM(2099,2100) = 4407900

Factors of 2099

List of positive integer factors of 2099 that divides 2099 without a remainder.

1, 2099

Factors of 2100

List of positive integer factors of 2100 that divides 2100 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100

Least Common Multiple of 2099 and 2100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2099 and 2100, than apply into the LCM equation.

GCF(2099,2100) = 1
LCM(2099,2100) = ( 2099 × 2100) / 1
LCM(2099,2100) = 4407900 / 1
LCM(2099,2100) = 4407900

Properties of LCM 2099 and 2100

(i) The LCM of 2100 and 2099 is associative

LCM of 2099 and 2100 = LCM of 2100 and 2099

Related Least Common Multiples of 2099

Related Least Common Multiples of 2100

Frequently Asked Questions on LCM of 2099 and 2100

1. What is the LCM of 2099 and 2100?

Answer: LCM of 2099 and 2100 is 4407900.

2. What are the Factors of 2099?

Answer: Factors of 2099 are 1, 2099. There are 2 integers that are factors of 2099. The greatest factor of 2099 is 2099.

3. What are the Factors of 2100?

Answer: Factors of 2100 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050, 2100. There are 36 integers that are factors of 2100. The greatest factor of 2100 is 2100.

4. How to Find the LCM of 2099 and 2100?

Answer:

Least Common Multiple of 2099 and 2100 = 4407900

Step 1: Find the prime factorization of 2099

2099 = 2099

Step 2: Find the prime factorization of 2100

2100 = 2 x 2 x 3 x 5 x 5 x 7

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

LCM = 4407900 = 2 x 2 x 3 x 5 x 5 x 7 x 2099

Step 4: Therefore, the least common multiple of 2099 and 2100 is 4407900.