Least Common Multiple of 2100 and 2106

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 2106 the smallest integer that is 737100 that is divisible by both numbers.

Least Common Multiple (LCM) of 2100 and 2106 is 737100.

LCM(2100,2106) = 737100

LCM of 2100 and 2106

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

LCM of:
and

Least Common Multiple of 2100 and 2106

LCM of 2100 and 2106 is 737100

Least common multiple can be found by multiplying the highest exponent prime factors of 2100 and 2106. First we will calculate the prime factors of 2100 and 2106.

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 2106


2 2106
3 1053
3 351
3 117
3 39
13 13
1

Prime factors of 2106 are 2, 3,13. Prime factorization of 2106 in exponential form is:

2106 = 21×34×131

Now multiplying the highest exponent prime factors to calculate the LCM of 2100 and 2106.

LCM(2100,2106) = 22×34×52×71×131
LCM(2100,2106) = 737100

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 2106

List of positive integer factors of 2106 that divides 2106 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 234, 351, 702, 1053, 2106

Least Common Multiple of 2100 and 2106 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 2106, than apply into the LCM equation.

GCF(2100,2106) = 6
LCM(2100,2106) = ( 2100 × 2106) / 6
LCM(2100,2106) = 4422600 / 6
LCM(2100,2106) = 737100

Properties of LCM 2100 and 2106

(i) The LCM of 2106 and 2100 is associative

LCM of 2100 and 2106 = LCM of 2106 and 2100

Related Least Common Multiples of 2100

Related Least Common Multiples of 2106

Frequently Asked Questions on LCM of 2100 and 2106

1. What is the LCM of 2100 and 2106?

Answer: LCM of 2100 and 2106 is 737100.

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 2106?

Answer: Factors of 2106 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 234, 351, 702, 1053, 2106. There are 20 integers that are factors of 2106. The greatest factor of 2106 is 2106.

4. How to Find the LCM of 2100 and 2106?

Answer:

Least Common Multiple of 2100 and 2106 = 737100

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 2106

2106 = 2 x 3 x 3 x 3 x 3 x 13

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

LCM = 737100 = 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5 x 7 x 13

Step 4: Therefore, the least common multiple of 2100 and 2106 is 737100.