Least Common Multiple of 96 and 100

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 96 and 100 the smallest integer that is 2400 that is divisible by both numbers.

Least Common Multiple (LCM) of 96 and 100 is 2400.

LCM(96,100) = 2400

LCM of 96 and 100

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

LCM of:
and

Least Common Multiple of 96 and 100

LCM of 96 and 100 is 2400

Least common multiple can be found by multiplying the highest exponent prime factors of 96 and 100. First we will calculate the prime factors of 96 and 100.

Prime Factorization of 96


2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 96 are 2,3. Prime factorization of 96 in exponential form is:

96 = 25×31

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

Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 100.

LCM(96,100) = 25×31×52
LCM(96,100) = 2400

Factors of 96

List of positive integer factors of 96 that divides 96 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

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

Least Common Multiple of 96 and 100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 96 and 100, than apply into the LCM equation.

GCF(96,100) = 4
LCM(96,100) = ( 96 × 100) / 4
LCM(96,100) = 9600 / 4
LCM(96,100) = 2400

Properties of LCM 96 and 100

(i) The LCM of 100 and 96 is associative

LCM of 96 and 100 = LCM of 100 and 96

Related Least Common Multiples of 96

Related Least Common Multiples of 100

Frequently Asked Questions on LCM of 96 and 100

1. What is the LCM of 96 and 100?

Answer: LCM of 96 and 100 is 2400.

2. What are the Factors of 96?

Answer: Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. There are 12 integers that are factors of 96. The greatest factor of 96 is 96.

3. 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.

4. How to Find the LCM of 96 and 100?

Answer:

Least Common Multiple of 96 and 100 = 2400

Step 1: Find the prime factorization of 96

96 = 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 100

100 = 2 x 2 x 5 x 5

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

LCM = 2400 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 96 and 100 is 2400.