Least Common Multiple of 112 and 114

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 114 the smallest integer that is 6384 that is divisible by both numbers.

Least Common Multiple (LCM) of 112 and 114 is 6384.

LCM(112,114) = 6384

LCM of 112 and 114

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

LCM of:
and

Least Common Multiple of 112 and 114

LCM of 112 and 114 is 6384

Least common multiple can be found by multiplying the highest exponent prime factors of 112 and 114. First we will calculate the prime factors of 112 and 114.

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 114


2 114
3 57
19 19
1

Prime factors of 114 are 2, 3,19. Prime factorization of 114 in exponential form is:

114 = 21×31×191

Now multiplying the highest exponent prime factors to calculate the LCM of 112 and 114.

LCM(112,114) = 24×31×71×191
LCM(112,114) = 6384

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 114

List of positive integer factors of 114 that divides 114 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114

Least Common Multiple of 112 and 114 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 114, than apply into the LCM equation.

GCF(112,114) = 2
LCM(112,114) = ( 112 × 114) / 2
LCM(112,114) = 12768 / 2
LCM(112,114) = 6384

Properties of LCM 112 and 114

(i) The LCM of 114 and 112 is associative

LCM of 112 and 114 = LCM of 114 and 112

Related Least Common Multiples of 112

Related Least Common Multiples of 114

Frequently Asked Questions on LCM of 112 and 114

1. What is the LCM of 112 and 114?

Answer: LCM of 112 and 114 is 6384.

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 114?

Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.

4. How to Find the LCM of 112 and 114?

Answer:

Least Common Multiple of 112 and 114 = 6384

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 114

114 = 2 x 3 x 19

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

LCM = 6384 = 2 x 2 x 2 x 2 x 3 x 7 x 19

Step 4: Therefore, the least common multiple of 112 and 114 is 6384.