Least Common Multiple of 114 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 114 and 115 the smallest integer that is 13110 that is divisible by both numbers.

Least Common Multiple (LCM) of 114 and 115 is 13110.

LCM(114,115) = 13110

LCM of 114 and 115

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

LCM of:
and

Least Common Multiple of 114 and 115

LCM of 114 and 115 is 13110

Least common multiple can be found by multiplying the highest exponent prime factors of 114 and 115. First we will calculate the prime factors of 114 and 115.

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

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 114 and 115.

LCM(114,115) = 21×31×51×191×231
LCM(114,115) = 13110

Factors of 114

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

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

Factors of 115

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

1, 5, 23, 115

Least Common Multiple of 114 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 114 and 115, than apply into the LCM equation.

GCF(114,115) = 1
LCM(114,115) = ( 114 × 115) / 1
LCM(114,115) = 13110 / 1
LCM(114,115) = 13110

Properties of LCM 114 and 115

(i) The LCM of 115 and 114 is associative

LCM of 114 and 115 = LCM of 115 and 114

Related Least Common Multiples of 114

Related Least Common Multiples of 115

Frequently Asked Questions on LCM of 114 and 115

1. What is the LCM of 114 and 115?

Answer: LCM of 114 and 115 is 13110.

2. 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.

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 114 and 115?

Answer:

Least Common Multiple of 114 and 115 = 13110

Step 1: Find the prime factorization of 114

114 = 2 x 3 x 19

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 = 13110 = 2 x 3 x 5 x 19 x 23

Step 4: Therefore, the least common multiple of 114 and 115 is 13110.