Least Common Multiple of 2096 and 2100

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2096 and 2100 the smallest integer that is 1100400 that is divisible by both numbers.

Least Common Multiple (LCM) of 2096 and 2100 is 1100400.

LCM(2096,2100) = 1100400

LCM of 2096 and 2100

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

LCM of:
and

Least Common Multiple of 2096 and 2100

LCM of 2096 and 2100 is 1100400

Least common multiple can be found by multiplying the highest exponent prime factors of 2096 and 2100. First we will calculate the prime factors of 2096 and 2100.

Prime Factorization of 2096


2 2096
2 1048
2 524
2 262
131 131
1

Prime factors of 2096 are 2,131. Prime factorization of 2096 in exponential form is:

2096 = 24×1311

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

Now multiplying the highest exponent prime factors to calculate the LCM of 2096 and 2100.

LCM(2096,2100) = 24×31×52×71×1311
LCM(2096,2100) = 1100400

Factors of 2096

List of positive integer factors of 2096 that divides 2096 without a remainder.

1, 2, 4, 8, 16, 131, 262, 524, 1048, 2096

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

Least Common Multiple of 2096 and 2100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2096 and 2100, than apply into the LCM equation.

GCF(2096,2100) = 4
LCM(2096,2100) = ( 2096 × 2100) / 4
LCM(2096,2100) = 4401600 / 4
LCM(2096,2100) = 1100400

Properties of LCM 2096 and 2100

(i) The LCM of 2100 and 2096 is associative

LCM of 2096 and 2100 = LCM of 2100 and 2096

Related Least Common Multiples of 2096

Related Least Common Multiples of 2100

Frequently Asked Questions on LCM of 2096 and 2100

1. What is the LCM of 2096 and 2100?

Answer: LCM of 2096 and 2100 is 1100400.

2. What are the Factors of 2096?

Answer: Factors of 2096 are 1, 2, 4, 8, 16, 131, 262, 524, 1048, 2096. There are 10 integers that are factors of 2096. The greatest factor of 2096 is 2096.

3. 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.

4. How to Find the LCM of 2096 and 2100?

Answer:

Least Common Multiple of 2096 and 2100 = 1100400

Step 1: Find the prime factorization of 2096

2096 = 2 x 2 x 2 x 2 x 131

Step 2: Find the prime factorization of 2100

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

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

LCM = 1100400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 131

Step 4: Therefore, the least common multiple of 2096 and 2100 is 1100400.