Least Common Multiple of 112 and 115

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 115 the smallest integer that is 12880 that is divisible by both numbers.

Least Common Multiple (LCM) of 112 and 115 is 12880.

LCM(112,115) = 12880

LCM of 112 and 115

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

LCM of:
and

Least Common Multiple of 112 and 115

LCM of 112 and 115 is 12880

Least common multiple can be found by multiplying the highest exponent prime factors of 112 and 115. First we will calculate the prime factors of 112 and 115.

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 115


5 115
23 23
1

Prime factors of 115 are 5,23. Prime factorization of 115 in exponential form is:

115 = 51×231

Now multiplying the highest exponent prime factors to calculate the LCM of 112 and 115.

LCM(112,115) = 24×51×71×231
LCM(112,115) = 12880

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 115

List of positive integer factors of 115 that divides 115 without a remainder.

1, 5, 23, 115

Least Common Multiple of 112 and 115 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 115, than apply into the LCM equation.

GCF(112,115) = 1
LCM(112,115) = ( 112 × 115) / 1
LCM(112,115) = 12880 / 1
LCM(112,115) = 12880

Properties of LCM 112 and 115

(i) The LCM of 115 and 112 is associative

LCM of 112 and 115 = LCM of 115 and 112

Related Least Common Multiples of 112

Related Least Common Multiples of 115

Frequently Asked Questions on LCM of 112 and 115

1. What is the LCM of 112 and 115?

Answer: LCM of 112 and 115 is 12880.

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 115?

Answer: Factors of 115 are 1, 5, 23, 115. There are 4 integers that are factors of 115. The greatest factor of 115 is 115.

4. How to Find the LCM of 112 and 115?

Answer:

Least Common Multiple of 112 and 115 = 12880

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 115

115 = 5 x 23

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

LCM = 12880 = 2 x 2 x 2 x 2 x 5 x 7 x 23

Step 4: Therefore, the least common multiple of 112 and 115 is 12880.