Least Common Multiple of 108 and 112

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 108 and 112 the smallest integer that is 3024 that is divisible by both numbers.

Least Common Multiple (LCM) of 108 and 112 is 3024.

LCM(108,112) = 3024

LCM of 108 and 112

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

LCM of:
and

Least Common Multiple of 108 and 112

LCM of 108 and 112 is 3024

Least common multiple can be found by multiplying the highest exponent prime factors of 108 and 112. First we will calculate the prime factors of 108 and 112.

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

Prime Factorization of 112


2 112
2 56
2 28
2 14
7 7
1

Prime factors of 112 are 2,7. Prime factorization of 112 in exponential form is:

112 = 24×71

Now multiplying the highest exponent prime factors to calculate the LCM of 108 and 112.

LCM(108,112) = 24×33×71
LCM(108,112) = 3024

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

Factors of 112

List of positive integer factors of 112 that divides 112 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112

Least Common Multiple of 108 and 112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 108 and 112, than apply into the LCM equation.

GCF(108,112) = 4
LCM(108,112) = ( 108 × 112) / 4
LCM(108,112) = 12096 / 4
LCM(108,112) = 3024

Properties of LCM 108 and 112

(i) The LCM of 112 and 108 is associative

LCM of 108 and 112 = LCM of 112 and 108

Related Least Common Multiples of 108

Related Least Common Multiples of 112

Frequently Asked Questions on LCM of 108 and 112

1. What is the LCM of 108 and 112?

Answer: LCM of 108 and 112 is 3024.

2. 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.

3. What are the Factors of 112?

Answer: Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112. There are 10 integers that are factors of 112. The greatest factor of 112 is 112.

4. How to Find the LCM of 108 and 112?

Answer:

Least Common Multiple of 108 and 112 = 3024

Step 1: Find the prime factorization of 108

108 = 2 x 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 112

112 = 2 x 2 x 2 x 2 x 7

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

LCM = 3024 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 108 and 112 is 3024.