Least Common Multiple of 96 and 111

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 111 the smallest integer that is 3552 that is divisible by both numbers.

Least Common Multiple (LCM) of 96 and 111 is 3552.

LCM(96,111) = 3552

LCM of 96 and 111

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

LCM of:
and

Least Common Multiple of 96 and 111

LCM of 96 and 111 is 3552

Least common multiple can be found by multiplying the highest exponent prime factors of 96 and 111. First we will calculate the prime factors of 96 and 111.

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 111


3 111
37 37
1

Prime factors of 111 are 3,37. Prime factorization of 111 in exponential form is:

111 = 31×371

Now multiplying the highest exponent prime factors to calculate the LCM of 96 and 111.

LCM(96,111) = 25×31×371
LCM(96,111) = 3552

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 111

List of positive integer factors of 111 that divides 111 without a remainder.

1, 3, 37, 111

Least Common Multiple of 96 and 111 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 111, than apply into the LCM equation.

GCF(96,111) = 3
LCM(96,111) = ( 96 × 111) / 3
LCM(96,111) = 10656 / 3
LCM(96,111) = 3552

Properties of LCM 96 and 111

(i) The LCM of 111 and 96 is associative

LCM of 96 and 111 = LCM of 111 and 96

Related Least Common Multiples of 96

Related Least Common Multiples of 111

Frequently Asked Questions on LCM of 96 and 111

1. What is the LCM of 96 and 111?

Answer: LCM of 96 and 111 is 3552.

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 111?

Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.

4. How to Find the LCM of 96 and 111?

Answer:

Least Common Multiple of 96 and 111 = 3552

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 111

111 = 3 x 37

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

LCM = 3552 = 2 x 2 x 2 x 2 x 2 x 3 x 37

Step 4: Therefore, the least common multiple of 96 and 111 is 3552.