Least Common Multiple of 2100 and 2101

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 2101 the smallest integer that is 4412100 that is divisible by both numbers.

Least Common Multiple (LCM) of 2100 and 2101 is 4412100.

LCM(2100,2101) = 4412100

LCM of 2100 and 2101

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

LCM of:
and

Least Common Multiple of 2100 and 2101

LCM of 2100 and 2101 is 4412100

Least common multiple can be found by multiplying the highest exponent prime factors of 2100 and 2101. First we will calculate the prime factors of 2100 and 2101.

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 2101


11 2101
191 191
1

Prime factors of 2101 are 11,191. Prime factorization of 2101 in exponential form is:

2101 = 111×1911

Now multiplying the highest exponent prime factors to calculate the LCM of 2100 and 2101.

LCM(2100,2101) = 22×31×52×71×111×1911
LCM(2100,2101) = 4412100

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 2101

List of positive integer factors of 2101 that divides 2101 without a remainder.

1, 11, 191, 2101

Least Common Multiple of 2100 and 2101 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 2101, than apply into the LCM equation.

GCF(2100,2101) = 1
LCM(2100,2101) = ( 2100 × 2101) / 1
LCM(2100,2101) = 4412100 / 1
LCM(2100,2101) = 4412100

Properties of LCM 2100 and 2101

(i) The LCM of 2101 and 2100 is associative

LCM of 2100 and 2101 = LCM of 2101 and 2100

Related Least Common Multiples of 2100

Related Least Common Multiples of 2101

Frequently Asked Questions on LCM of 2100 and 2101

1. What is the LCM of 2100 and 2101?

Answer: LCM of 2100 and 2101 is 4412100.

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 2101?

Answer: Factors of 2101 are 1, 11, 191, 2101. There are 4 integers that are factors of 2101. The greatest factor of 2101 is 2101.

4. How to Find the LCM of 2100 and 2101?

Answer:

Least Common Multiple of 2100 and 2101 = 4412100

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 2101

2101 = 11 x 191

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

LCM = 4412100 = 2 x 2 x 3 x 5 x 5 x 7 x 11 x 191

Step 4: Therefore, the least common multiple of 2100 and 2101 is 4412100.