Least Common Multiple of 108 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 108 and 116 the smallest integer that is 3132 that is divisible by both numbers.

Least Common Multiple (LCM) of 108 and 116 is 3132.

LCM(108,116) = 3132

LCM of 108 and 116

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

LCM of:
and

Least Common Multiple of 108 and 116

LCM of 108 and 116 is 3132

Least common multiple can be found by multiplying the highest exponent prime factors of 108 and 116. First we will calculate the prime factors of 108 and 116.

Prime Factorization of 108


2 108
2 54
3 27
3 9
3 3
1

Prime factors of 108 are 2,3. Prime factorization of 108 in exponential form is:

108 = 22×33

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 108 and 116.

LCM(108,116) = 22×33×291
LCM(108,116) = 3132

Factors of 108

List of positive integer factors of 108 that divides 108 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

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 108 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 108 and 116, than apply into the LCM equation.

GCF(108,116) = 4
LCM(108,116) = ( 108 × 116) / 4
LCM(108,116) = 12528 / 4
LCM(108,116) = 3132

Properties of LCM 108 and 116

(i) The LCM of 116 and 108 is associative

LCM of 108 and 116 = LCM of 116 and 108

Related Least Common Multiples of 108

Related Least Common Multiples of 116

Frequently Asked Questions on LCM of 108 and 116

1. What is the LCM of 108 and 116?

Answer: LCM of 108 and 116 is 3132.

2. What are the Factors of 108?

Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.

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 108 and 116?

Answer:

Least Common Multiple of 108 and 116 = 3132

Step 1: Find the prime factorization of 108

108 = 2 x 2 x 3 x 3 x 3

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 = 3132 = 2 x 2 x 3 x 3 x 3 x 29

Step 4: Therefore, the least common multiple of 108 and 116 is 3132.