Least Common Multiple of 96 and 108

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 108 the smallest integer that is 864 that is divisible by both numbers.

Least Common Multiple (LCM) of 96 and 108 is 864.

LCM(96,108) = 864

LCM of 96 and 108

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

LCM of:
and

Least Common Multiple of 96 and 108

LCM of 96 and 108 is 864

Least common multiple can be found by multiplying the highest exponent prime factors of 96 and 108. First we will calculate the prime factors of 96 and 108.

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 108


2 108
2 54
3 27
3 9
3 3
1

Prime factors of 108 are 2,3. Prime factorization of 108 in exponential form is:

108 = 22×33

Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 108.

LCM(96,108) = 25×33
LCM(96,108) = 864

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 108

List of positive integer factors of 108 that divides 108 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

Least Common Multiple of 96 and 108 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 108, than apply into the LCM equation.

GCF(96,108) = 12
LCM(96,108) = ( 96 × 108) / 12
LCM(96,108) = 10368 / 12
LCM(96,108) = 864

Properties of LCM 96 and 108

(i) The LCM of 108 and 96 is associative

LCM of 96 and 108 = LCM of 108 and 96

Related Least Common Multiples of 96

Related Least Common Multiples of 108

Frequently Asked Questions on LCM of 96 and 108

1. What is the LCM of 96 and 108?

Answer: LCM of 96 and 108 is 864.

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 108?

Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.

4. How to Find the LCM of 96 and 108?

Answer:

Least Common Multiple of 96 and 108 = 864

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 108

108 = 2 x 2 x 3 x 3 x 3

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

LCM = 864 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Step 4: Therefore, the least common multiple of 96 and 108 is 864.