Least Common Multiple of 2100 and 2107

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 2107 the smallest integer that is 632100 that is divisible by both numbers.

Least Common Multiple (LCM) of 2100 and 2107 is 632100.

LCM(2100,2107) = 632100

LCM of 2100 and 2107

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

LCM of:
and

Least Common Multiple of 2100 and 2107

LCM of 2100 and 2107 is 632100

Least common multiple can be found by multiplying the highest exponent prime factors of 2100 and 2107. First we will calculate the prime factors of 2100 and 2107.

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 2107


7 2107
7 301
43 43
1

Prime factors of 2107 are 7,43. Prime factorization of 2107 in exponential form is:

2107 = 72×431

Now multiplying the highest exponent prime factors to calculate the LCM of 2100 and 2107.

LCM(2100,2107) = 22×31×52×72×431
LCM(2100,2107) = 632100

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 2107

List of positive integer factors of 2107 that divides 2107 without a remainder.

1, 7, 43, 49, 301, 2107

Least Common Multiple of 2100 and 2107 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 2107, than apply into the LCM equation.

GCF(2100,2107) = 7
LCM(2100,2107) = ( 2100 × 2107) / 7
LCM(2100,2107) = 4424700 / 7
LCM(2100,2107) = 632100

Properties of LCM 2100 and 2107

(i) The LCM of 2107 and 2100 is associative

LCM of 2100 and 2107 = LCM of 2107 and 2100

Related Least Common Multiples of 2100

Related Least Common Multiples of 2107

Frequently Asked Questions on LCM of 2100 and 2107

1. What is the LCM of 2100 and 2107?

Answer: LCM of 2100 and 2107 is 632100.

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 2107?

Answer: Factors of 2107 are 1, 7, 43, 49, 301, 2107. There are 6 integers that are factors of 2107. The greatest factor of 2107 is 2107.

4. How to Find the LCM of 2100 and 2107?

Answer:

Least Common Multiple of 2100 and 2107 = 632100

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 2107

2107 = 7 x 7 x 43

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

LCM = 632100 = 2 x 2 x 3 x 5 x 5 x 7 x 7 x 43

Step 4: Therefore, the least common multiple of 2100 and 2107 is 632100.