Least Common Multiple of 100 and 101

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 100 and 101 the smallest integer that is 10100 that is divisible by both numbers.

Least Common Multiple (LCM) of 100 and 101 is 10100.

LCM(100,101) = 10100

LCM of 100 and 101

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

LCM of:
and

Least Common Multiple of 100 and 101

LCM of 100 and 101 is 10100

Least common multiple can be found by multiplying the highest exponent prime factors of 100 and 101. First we will calculate the prime factors of 100 and 101.

Prime Factorization of 100


2 100
2 50
5 25
5 5
1

Prime factors of 100 are 2,5. Prime factorization of 100 in exponential form is:

100 = 22×52

Prime Factorization of 101


101 101
1

Prime factors of 101 are 101. Prime factorization of 101 in exponential form is:

101 = 1011

Now multiplying the highest exponent prime factors to calculate the LCM of 100 and 101.

LCM(100,101) = 22×52×1011
LCM(100,101) = 10100

Factors of 100

List of positive integer factors of 100 that divides 100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100

Factors of 101

List of positive integer factors of 101 that divides 101 without a remainder.

1, 101

Least Common Multiple of 100 and 101 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 100 and 101, than apply into the LCM equation.

GCF(100,101) = 1
LCM(100,101) = ( 100 × 101) / 1
LCM(100,101) = 10100 / 1
LCM(100,101) = 10100

Properties of LCM 100 and 101

(i) The LCM of 101 and 100 is associative

LCM of 100 and 101 = LCM of 101 and 100

Related Least Common Multiples of 100

Related Least Common Multiples of 101

Frequently Asked Questions on LCM of 100 and 101

1. What is the LCM of 100 and 101?

Answer: LCM of 100 and 101 is 10100.

2. What are the Factors of 100?

Answer: Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. There are 9 integers that are factors of 100. The greatest factor of 100 is 100.

3. What are the Factors of 101?

Answer: Factors of 101 are 1, 101. There are 2 integers that are factors of 101. The greatest factor of 101 is 101.

4. How to Find the LCM of 100 and 101?

Answer:

Least Common Multiple of 100 and 101 = 10100

Step 1: Find the prime factorization of 100

100 = 2 x 2 x 5 x 5

Step 2: Find the prime factorization of 101

101 = 101

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

LCM = 10100 = 2 x 2 x 5 x 5 x 101

Step 4: Therefore, the least common multiple of 100 and 101 is 10100.