Least Common Multiple of 2100 and 2103

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2100 and 2103 the smallest integer that is 1472100 that is divisible by both numbers.

Least Common Multiple (LCM) of 2100 and 2103 is 1472100.

LCM(2100,2103) = 1472100

LCM of 2100 and 2103

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

LCM of:
and

Least Common Multiple of 2100 and 2103

LCM of 2100 and 2103 is 1472100

Least common multiple can be found by multiplying the highest exponent prime factors of 2100 and 2103. First we will calculate the prime factors of 2100 and 2103.

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

Prime Factorization of 2103


3 2103
701 701
1

Prime factors of 2103 are 3,701. Prime factorization of 2103 in exponential form is:

2103 = 31×7011

Now multiplying the highest exponent prime factors to calculate the LCM of 2100 and 2103.

LCM(2100,2103) = 22×31×52×71×7011
LCM(2100,2103) = 1472100

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

Factors of 2103

List of positive integer factors of 2103 that divides 2103 without a remainder.

1, 3, 701, 2103

Least Common Multiple of 2100 and 2103 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2100 and 2103, than apply into the LCM equation.

GCF(2100,2103) = 3
LCM(2100,2103) = ( 2100 × 2103) / 3
LCM(2100,2103) = 4416300 / 3
LCM(2100,2103) = 1472100

Properties of LCM 2100 and 2103

(i) The LCM of 2103 and 2100 is associative

LCM of 2100 and 2103 = LCM of 2103 and 2100

Related Least Common Multiples of 2100

Related Least Common Multiples of 2103

Frequently Asked Questions on LCM of 2100 and 2103

1. What is the LCM of 2100 and 2103?

Answer: LCM of 2100 and 2103 is 1472100.

2. 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.

3. What are the Factors of 2103?

Answer: Factors of 2103 are 1, 3, 701, 2103. There are 4 integers that are factors of 2103. The greatest factor of 2103 is 2103.

4. How to Find the LCM of 2100 and 2103?

Answer:

Least Common Multiple of 2100 and 2103 = 1472100

Step 1: Find the prime factorization of 2100

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

Step 2: Find the prime factorization of 2103

2103 = 3 x 701

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

LCM = 1472100 = 2 x 2 x 3 x 5 x 5 x 7 x 701

Step 4: Therefore, the least common multiple of 2100 and 2103 is 1472100.