Least Common Multiple of 114 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 114 and 117 the smallest integer that is 4446 that is divisible by both numbers.

Least Common Multiple (LCM) of 114 and 117 is 4446.

LCM(114,117) = 4446

LCM of 114 and 117

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

LCM of:
and

Least Common Multiple of 114 and 117

LCM of 114 and 117 is 4446

Least common multiple can be found by multiplying the highest exponent prime factors of 114 and 117. First we will calculate the prime factors of 114 and 117.

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 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 114 and 117.

LCM(114,117) = 21×32×131×191
LCM(114,117) = 4446

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 117

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

1, 3, 9, 13, 39, 117

Least Common Multiple of 114 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 114 and 117, than apply into the LCM equation.

GCF(114,117) = 3
LCM(114,117) = ( 114 × 117) / 3
LCM(114,117) = 13338 / 3
LCM(114,117) = 4446

Properties of LCM 114 and 117

(i) The LCM of 117 and 114 is associative

LCM of 114 and 117 = LCM of 117 and 114

Related Least Common Multiples of 114

Related Least Common Multiples of 117

Frequently Asked Questions on LCM of 114 and 117

1. What is the LCM of 114 and 117?

Answer: LCM of 114 and 117 is 4446.

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 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 114 and 117?

Answer:

Least Common Multiple of 114 and 117 = 4446

Step 1: Find the prime factorization of 114

114 = 2 x 3 x 19

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 = 4446 = 2 x 3 x 3 x 13 x 19

Step 4: Therefore, the least common multiple of 114 and 117 is 4446.