Least Common Multiple of 10100 and 10104

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 10104 the smallest integer that is 25512600 that is divisible by both numbers.

Least Common Multiple (LCM) of 10100 and 10104 is 25512600.

LCM(10100,10104) = 25512600

LCM of 10100 and 10104

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

LCM of:
and

Least Common Multiple of 10100 and 10104

LCM of 10100 and 10104 is 25512600

Least common multiple can be found by multiplying the highest exponent prime factors of 10100 and 10104. First we will calculate the prime factors of 10100 and 10104.

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 10104


2 10104
2 5052
2 2526
3 1263
421 421
1

Prime factors of 10104 are 2, 3,421. Prime factorization of 10104 in exponential form is:

10104 = 23×31×4211

Now multiplying the highest exponent prime factors to calculate the LCM of 10100 and 10104.

LCM(10100,10104) = 23×31×52×1011×4211
LCM(10100,10104) = 25512600

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 10104

List of positive integer factors of 10104 that divides 10104 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 421, 842, 1263, 1684, 2526, 3368, 5052, 10104

Least Common Multiple of 10100 and 10104 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 10104, than apply into the LCM equation.

GCF(10100,10104) = 4
LCM(10100,10104) = ( 10100 × 10104) / 4
LCM(10100,10104) = 102050400 / 4
LCM(10100,10104) = 25512600

Properties of LCM 10100 and 10104

(i) The LCM of 10104 and 10100 is associative

LCM of 10100 and 10104 = LCM of 10104 and 10100

Related Least Common Multiples of 10100

Related Least Common Multiples of 10104

Frequently Asked Questions on LCM of 10100 and 10104

1. What is the LCM of 10100 and 10104?

Answer: LCM of 10100 and 10104 is 25512600.

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 10104?

Answer: Factors of 10104 are 1, 2, 3, 4, 6, 8, 12, 24, 421, 842, 1263, 1684, 2526, 3368, 5052, 10104. There are 16 integers that are factors of 10104. The greatest factor of 10104 is 10104.

4. How to Find the LCM of 10100 and 10104?

Answer:

Least Common Multiple of 10100 and 10104 = 25512600

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 10104

10104 = 2 x 2 x 2 x 3 x 421

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

LCM = 25512600 = 2 x 2 x 2 x 3 x 5 x 5 x 101 x 421

Step 4: Therefore, the least common multiple of 10100 and 10104 is 25512600.