Least Common Multiple of 108 and 114

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 114 the smallest integer that is 2052 that is divisible by both numbers.

Least Common Multiple (LCM) of 108 and 114 is 2052.

LCM(108,114) = 2052

LCM of 108 and 114

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

LCM of:
and

Least Common Multiple of 108 and 114

LCM of 108 and 114 is 2052

Least common multiple can be found by multiplying the highest exponent prime factors of 108 and 114. First we will calculate the prime factors of 108 and 114.

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 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

Now multiplying the highest exponent prime factors to calculate the LCM of 108 and 114.

LCM(108,114) = 22×33×191
LCM(108,114) = 2052

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 114

List of positive integer factors of 114 that divides 114 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114

Least Common Multiple of 108 and 114 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 114, than apply into the LCM equation.

GCF(108,114) = 6
LCM(108,114) = ( 108 × 114) / 6
LCM(108,114) = 12312 / 6
LCM(108,114) = 2052

Properties of LCM 108 and 114

(i) The LCM of 114 and 108 is associative

LCM of 108 and 114 = LCM of 114 and 108

Related Least Common Multiples of 108

Related Least Common Multiples of 114

Frequently Asked Questions on LCM of 108 and 114

1. What is the LCM of 108 and 114?

Answer: LCM of 108 and 114 is 2052.

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 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.

4. How to Find the LCM of 108 and 114?

Answer:

Least Common Multiple of 108 and 114 = 2052

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 114

114 = 2 x 3 x 19

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

LCM = 2052 = 2 x 2 x 3 x 3 x 3 x 19

Step 4: Therefore, the least common multiple of 108 and 114 is 2052.