Least Common Multiple of 117 and 118

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 117 and 118 the smallest integer that is 13806 that is divisible by both numbers.

Least Common Multiple (LCM) of 117 and 118 is 13806.

LCM(117,118) = 13806

LCM of 117 and 118

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

LCM of:
and

Least Common Multiple of 117 and 118

LCM of 117 and 118 is 13806

Least common multiple can be found by multiplying the highest exponent prime factors of 117 and 118. First we will calculate the prime factors of 117 and 118.

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

Prime Factorization of 118


2 118
59 59
1

Prime factors of 118 are 2,59. Prime factorization of 118 in exponential form is:

118 = 21×591

Now multiplying the highest exponent prime factors to calculate the LCM of 117 and 118.

LCM(117,118) = 21×32×131×591
LCM(117,118) = 13806

Factors of 117

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

1, 3, 9, 13, 39, 117

Factors of 118

List of positive integer factors of 118 that divides 118 without a remainder.

1, 2, 59, 118

Least Common Multiple of 117 and 118 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 117 and 118, than apply into the LCM equation.

GCF(117,118) = 1
LCM(117,118) = ( 117 × 118) / 1
LCM(117,118) = 13806 / 1
LCM(117,118) = 13806

Properties of LCM 117 and 118

(i) The LCM of 118 and 117 is associative

LCM of 117 and 118 = LCM of 118 and 117

Related Least Common Multiples of 117

Related Least Common Multiples of 118

Frequently Asked Questions on LCM of 117 and 118

1. What is the LCM of 117 and 118?

Answer: LCM of 117 and 118 is 13806.

2. 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.

3. What are the Factors of 118?

Answer: Factors of 118 are 1, 2, 59, 118. There are 4 integers that are factors of 118. The greatest factor of 118 is 118.

4. How to Find the LCM of 117 and 118?

Answer:

Least Common Multiple of 117 and 118 = 13806

Step 1: Find the prime factorization of 117

117 = 3 x 3 x 13

Step 2: Find the prime factorization of 118

118 = 2 x 59

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

LCM = 13806 = 2 x 3 x 3 x 13 x 59

Step 4: Therefore, the least common multiple of 117 and 118 is 13806.