Least Common Multiple of 2100 and 2104

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 2104 the smallest integer that is 1104600 that is divisible by both numbers.

Least Common Multiple (LCM) of 2100 and 2104 is 1104600.

LCM(2100,2104) = 1104600

LCM of 2100 and 2104

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

LCM of:
and

Least Common Multiple of 2100 and 2104

LCM of 2100 and 2104 is 1104600

Least common multiple can be found by multiplying the highest exponent prime factors of 2100 and 2104. First we will calculate the prime factors of 2100 and 2104.

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 2104


2 2104
2 1052
2 526
263 263
1

Prime factors of 2104 are 2,263. Prime factorization of 2104 in exponential form is:

2104 = 23×2631

Now multiplying the highest exponent prime factors to calculate the LCM of 2100 and 2104.

LCM(2100,2104) = 23×31×52×71×2631
LCM(2100,2104) = 1104600

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 2104

List of positive integer factors of 2104 that divides 2104 without a remainder.

1, 2, 4, 8, 263, 526, 1052, 2104

Least Common Multiple of 2100 and 2104 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 2104, than apply into the LCM equation.

GCF(2100,2104) = 4
LCM(2100,2104) = ( 2100 × 2104) / 4
LCM(2100,2104) = 4418400 / 4
LCM(2100,2104) = 1104600

Properties of LCM 2100 and 2104

(i) The LCM of 2104 and 2100 is associative

LCM of 2100 and 2104 = LCM of 2104 and 2100

Related Least Common Multiples of 2100

Related Least Common Multiples of 2104

Frequently Asked Questions on LCM of 2100 and 2104

1. What is the LCM of 2100 and 2104?

Answer: LCM of 2100 and 2104 is 1104600.

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 2104?

Answer: Factors of 2104 are 1, 2, 4, 8, 263, 526, 1052, 2104. There are 8 integers that are factors of 2104. The greatest factor of 2104 is 2104.

4. How to Find the LCM of 2100 and 2104?

Answer:

Least Common Multiple of 2100 and 2104 = 1104600

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 2104

2104 = 2 x 2 x 2 x 263

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

LCM = 1104600 = 2 x 2 x 2 x 3 x 5 x 5 x 7 x 263

Step 4: Therefore, the least common multiple of 2100 and 2104 is 1104600.