Least Common Multiple of 116 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 116 and 117 the smallest integer that is 13572 that is divisible by both numbers.

Least Common Multiple (LCM) of 116 and 117 is 13572.

LCM(116,117) = 13572

LCM of 116 and 117

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

LCM of:
and

Least Common Multiple of 116 and 117

LCM of 116 and 117 is 13572

Least common multiple can be found by multiplying the highest exponent prime factors of 116 and 117. First we will calculate the prime factors of 116 and 117.

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

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 116 and 117.

LCM(116,117) = 22×32×131×291
LCM(116,117) = 13572

Factors of 116

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

1, 2, 4, 29, 58, 116

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 116 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 116 and 117, than apply into the LCM equation.

GCF(116,117) = 1
LCM(116,117) = ( 116 × 117) / 1
LCM(116,117) = 13572 / 1
LCM(116,117) = 13572

Properties of LCM 116 and 117

(i) The LCM of 117 and 116 is associative

LCM of 116 and 117 = LCM of 117 and 116

Related Least Common Multiples of 116

Related Least Common Multiples of 117

Frequently Asked Questions on LCM of 116 and 117

1. What is the LCM of 116 and 117?

Answer: LCM of 116 and 117 is 13572.

2. 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.

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 116 and 117?

Answer:

Least Common Multiple of 116 and 117 = 13572

Step 1: Find the prime factorization of 116

116 = 2 x 2 x 29

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 = 13572 = 2 x 2 x 3 x 3 x 13 x 29

Step 4: Therefore, the least common multiple of 116 and 117 is 13572.