Least Common Multiple of 112 and 117

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 112 and 117 the smallest integer that is 13104 that is divisible by both numbers.

Least Common Multiple (LCM) of 112 and 117 is 13104.

LCM(112,117) = 13104

LCM of 112 and 117

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

LCM of:
and

Least Common Multiple of 112 and 117

LCM of 112 and 117 is 13104

Least common multiple can be found by multiplying the highest exponent prime factors of 112 and 117. First we will calculate the prime factors of 112 and 117.

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

Prime Factorization of 117


3 117
3 39
13 13
1

Prime factors of 117 are 3,13. Prime factorization of 117 in exponential form is:

117 = 32×131

Now multiplying the highest exponent prime factors to calculate the LCM of 112 and 117.

LCM(112,117) = 24×32×71×131
LCM(112,117) = 13104

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

Factors of 117

List of positive integer factors of 117 that divides 117 without a remainder.

1, 3, 9, 13, 39, 117

Least Common Multiple of 112 and 117 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 112 and 117, than apply into the LCM equation.

GCF(112,117) = 1
LCM(112,117) = ( 112 × 117) / 1
LCM(112,117) = 13104 / 1
LCM(112,117) = 13104

Properties of LCM 112 and 117

(i) The LCM of 117 and 112 is associative

LCM of 112 and 117 = LCM of 117 and 112

Related Least Common Multiples of 112

Related Least Common Multiples of 117

Frequently Asked Questions on LCM of 112 and 117

1. What is the LCM of 112 and 117?

Answer: LCM of 112 and 117 is 13104.

2. 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.

3. What are the Factors of 117?

Answer: Factors of 117 are 1, 3, 9, 13, 39, 117. There are 6 integers that are factors of 117. The greatest factor of 117 is 117.

4. How to Find the LCM of 112 and 117?

Answer:

Least Common Multiple of 112 and 117 = 13104

Step 1: Find the prime factorization of 112

112 = 2 x 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 117

117 = 3 x 3 x 13

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

LCM = 13104 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 13

Step 4: Therefore, the least common multiple of 112 and 117 is 13104.