Least Common Multiple of 2100 and 2108

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 2108 the smallest integer that is 1106700 that is divisible by both numbers.

Least Common Multiple (LCM) of 2100 and 2108 is 1106700.

LCM(2100,2108) = 1106700

LCM of 2100 and 2108

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

LCM of:
and

Least Common Multiple of 2100 and 2108

LCM of 2100 and 2108 is 1106700

Least common multiple can be found by multiplying the highest exponent prime factors of 2100 and 2108. First we will calculate the prime factors of 2100 and 2108.

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 2108


2 2108
2 1054
17 527
31 31
1

Prime factors of 2108 are 2, 17,31. Prime factorization of 2108 in exponential form is:

2108 = 22×171×311

Now multiplying the highest exponent prime factors to calculate the LCM of 2100 and 2108.

LCM(2100,2108) = 22×31×52×71×171×311
LCM(2100,2108) = 1106700

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 2108

List of positive integer factors of 2108 that divides 2108 without a remainder.

1, 2, 4, 17, 31, 34, 62, 68, 124, 527, 1054, 2108

Least Common Multiple of 2100 and 2108 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 2108, than apply into the LCM equation.

GCF(2100,2108) = 4
LCM(2100,2108) = ( 2100 × 2108) / 4
LCM(2100,2108) = 4426800 / 4
LCM(2100,2108) = 1106700

Properties of LCM 2100 and 2108

(i) The LCM of 2108 and 2100 is associative

LCM of 2100 and 2108 = LCM of 2108 and 2100

Related Least Common Multiples of 2100

Related Least Common Multiples of 2108

Frequently Asked Questions on LCM of 2100 and 2108

1. What is the LCM of 2100 and 2108?

Answer: LCM of 2100 and 2108 is 1106700.

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 2108?

Answer: Factors of 2108 are 1, 2, 4, 17, 31, 34, 62, 68, 124, 527, 1054, 2108. There are 12 integers that are factors of 2108. The greatest factor of 2108 is 2108.

4. How to Find the LCM of 2100 and 2108?

Answer:

Least Common Multiple of 2100 and 2108 = 1106700

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 2108

2108 = 2 x 2 x 17 x 31

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

LCM = 1106700 = 2 x 2 x 3 x 5 x 5 x 7 x 17 x 31

Step 4: Therefore, the least common multiple of 2100 and 2108 is 1106700.