Least Common Multiple of 2098 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 2098 and 2100 the smallest integer that is 2202900 that is divisible by both numbers.

Least Common Multiple (LCM) of 2098 and 2100 is 2202900.

LCM(2098,2100) = 2202900

LCM of 2098 and 2100

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

LCM of:
and

Least Common Multiple of 2098 and 2100

LCM of 2098 and 2100 is 2202900

Least common multiple can be found by multiplying the highest exponent prime factors of 2098 and 2100. First we will calculate the prime factors of 2098 and 2100.

Prime Factorization of 2098


2 2098
1049 1049
1

Prime factors of 2098 are 2,1049. Prime factorization of 2098 in exponential form is:

2098 = 21×10491

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 2098 and 2100.

LCM(2098,2100) = 22×31×52×71×10491
LCM(2098,2100) = 2202900

Factors of 2098

List of positive integer factors of 2098 that divides 2098 without a remainder.

1, 2, 1049, 2098

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 2098 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 2098 and 2100, than apply into the LCM equation.

GCF(2098,2100) = 2
LCM(2098,2100) = ( 2098 × 2100) / 2
LCM(2098,2100) = 4405800 / 2
LCM(2098,2100) = 2202900

Properties of LCM 2098 and 2100

(i) The LCM of 2100 and 2098 is associative

LCM of 2098 and 2100 = LCM of 2100 and 2098

Related Least Common Multiples of 2098

Related Least Common Multiples of 2100

Frequently Asked Questions on LCM of 2098 and 2100

1. What is the LCM of 2098 and 2100?

Answer: LCM of 2098 and 2100 is 2202900.

2. What are the Factors of 2098?

Answer: Factors of 2098 are 1, 2, 1049, 2098. There are 4 integers that are factors of 2098. The greatest factor of 2098 is 2098.

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 2098 and 2100?

Answer:

Least Common Multiple of 2098 and 2100 = 2202900

Step 1: Find the prime factorization of 2098

2098 = 2 x 1049

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 = 2202900 = 2 x 2 x 3 x 5 x 5 x 7 x 1049

Step 4: Therefore, the least common multiple of 2098 and 2100 is 2202900.