Least Common Multiple of 10100 and 10108

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10100 and 10108 the smallest integer that is 25522700 that is divisible by both numbers.

Least Common Multiple (LCM) of 10100 and 10108 is 25522700.

LCM(10100,10108) = 25522700

LCM of 10100 and 10108

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

LCM of:
and

Least Common Multiple of 10100 and 10108

LCM of 10100 and 10108 is 25522700

Least common multiple can be found by multiplying the highest exponent prime factors of 10100 and 10108. First we will calculate the prime factors of 10100 and 10108.

Prime Factorization of 10100


2 10100
2 5050
5 2525
5 505
101 101
1

Prime factors of 10100 are 2, 5,101. Prime factorization of 10100 in exponential form is:

10100 = 22×52×1011

Prime Factorization of 10108


2 10108
2 5054
7 2527
19 361
19 19
1

Prime factors of 10108 are 2, 7,19. Prime factorization of 10108 in exponential form is:

10108 = 22×71×192

Now multiplying the highest exponent prime factors to calculate the LCM of 10100 and 10108.

LCM(10100,10108) = 22×52×71×192×1011
LCM(10100,10108) = 25522700

Factors of 10100

List of positive integer factors of 10100 that divides 10100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 101, 202, 404, 505, 1010, 2020, 2525, 5050, 10100

Factors of 10108

List of positive integer factors of 10108 that divides 10108 without a remainder.

1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 361, 532, 722, 1444, 2527, 5054, 10108

Least Common Multiple of 10100 and 10108 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10100 and 10108, than apply into the LCM equation.

GCF(10100,10108) = 4
LCM(10100,10108) = ( 10100 × 10108) / 4
LCM(10100,10108) = 102090800 / 4
LCM(10100,10108) = 25522700

Properties of LCM 10100 and 10108

(i) The LCM of 10108 and 10100 is associative

LCM of 10100 and 10108 = LCM of 10108 and 10100

Related Least Common Multiples of 10100

Related Least Common Multiples of 10108

Frequently Asked Questions on LCM of 10100 and 10108

1. What is the LCM of 10100 and 10108?

Answer: LCM of 10100 and 10108 is 25522700.

2. What are the Factors of 10100?

Answer: Factors of 10100 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 101, 202, 404, 505, 1010, 2020, 2525, 5050, 10100. There are 18 integers that are factors of 10100. The greatest factor of 10100 is 10100.

3. What are the Factors of 10108?

Answer: Factors of 10108 are 1, 2, 4, 7, 14, 19, 28, 38, 76, 133, 266, 361, 532, 722, 1444, 2527, 5054, 10108. There are 18 integers that are factors of 10108. The greatest factor of 10108 is 10108.

4. How to Find the LCM of 10100 and 10108?

Answer:

Least Common Multiple of 10100 and 10108 = 25522700

Step 1: Find the prime factorization of 10100

10100 = 2 x 2 x 5 x 5 x 101

Step 2: Find the prime factorization of 10108

10108 = 2 x 2 x 7 x 19 x 19

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

LCM = 25522700 = 2 x 2 x 5 x 5 x 7 x 19 x 19 x 101

Step 4: Therefore, the least common multiple of 10100 and 10108 is 25522700.