Least Common Multiple of 114 and 116

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 116 the smallest integer that is 6612 that is divisible by both numbers.

Least Common Multiple (LCM) of 114 and 116 is 6612.

LCM(114,116) = 6612

LCM of 114 and 116

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

LCM of:
and

Least Common Multiple of 114 and 116

LCM of 114 and 116 is 6612

Least common multiple can be found by multiplying the highest exponent prime factors of 114 and 116. First we will calculate the prime factors of 114 and 116.

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 116


2 116
2 58
29 29
1

Prime factors of 116 are 2,29. Prime factorization of 116 in exponential form is:

116 = 22×291

Now multiplying the highest exponent prime factors to calculate the LCM of 114 and 116.

LCM(114,116) = 22×31×191×291
LCM(114,116) = 6612

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 116

List of positive integer factors of 116 that divides 116 without a remainder.

1, 2, 4, 29, 58, 116

Least Common Multiple of 114 and 116 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 116, than apply into the LCM equation.

GCF(114,116) = 2
LCM(114,116) = ( 114 × 116) / 2
LCM(114,116) = 13224 / 2
LCM(114,116) = 6612

Properties of LCM 114 and 116

(i) The LCM of 116 and 114 is associative

LCM of 114 and 116 = LCM of 116 and 114

Related Least Common Multiples of 114

Related Least Common Multiples of 116

Frequently Asked Questions on LCM of 114 and 116

1. What is the LCM of 114 and 116?

Answer: LCM of 114 and 116 is 6612.

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 116?

Answer: Factors of 116 are 1, 2, 4, 29, 58, 116. There are 6 integers that are factors of 116. The greatest factor of 116 is 116.

4. How to Find the LCM of 114 and 116?

Answer:

Least Common Multiple of 114 and 116 = 6612

Step 1: Find the prime factorization of 114

114 = 2 x 3 x 19

Step 2: Find the prime factorization of 116

116 = 2 x 2 x 29

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

LCM = 6612 = 2 x 2 x 3 x 19 x 29

Step 4: Therefore, the least common multiple of 114 and 116 is 6612.