Least Common Multiple of 106 and 108

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 106 and 108 the smallest integer that is 5724 that is divisible by both numbers.

Least Common Multiple (LCM) of 106 and 108 is 5724.

LCM(106,108) = 5724

LCM of 106 and 108

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

LCM of:
and

Least Common Multiple of 106 and 108

LCM of 106 and 108 is 5724

Least common multiple can be found by multiplying the highest exponent prime factors of 106 and 108. First we will calculate the prime factors of 106 and 108.

Prime Factorization of 106


2 106
53 53
1

Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:

106 = 21×531

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

Now multiplying the highest exponent prime factors to calculate the LCM of 106 and 108.

LCM(106,108) = 22×33×531
LCM(106,108) = 5724

Factors of 106

List of positive integer factors of 106 that divides 106 without a remainder.

1, 2, 53, 106

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

Least Common Multiple of 106 and 108 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 106 and 108, than apply into the LCM equation.

GCF(106,108) = 2
LCM(106,108) = ( 106 × 108) / 2
LCM(106,108) = 11448 / 2
LCM(106,108) = 5724

Properties of LCM 106 and 108

(i) The LCM of 108 and 106 is associative

LCM of 106 and 108 = LCM of 108 and 106

Related Least Common Multiples of 106

Related Least Common Multiples of 108

Frequently Asked Questions on LCM of 106 and 108

1. What is the LCM of 106 and 108?

Answer: LCM of 106 and 108 is 5724.

2. What are the Factors of 106?

Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.

3. 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.

4. How to Find the LCM of 106 and 108?

Answer:

Least Common Multiple of 106 and 108 = 5724

Step 1: Find the prime factorization of 106

106 = 2 x 53

Step 2: Find the prime factorization of 108

108 = 2 x 2 x 3 x 3 x 3

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

LCM = 5724 = 2 x 2 x 3 x 3 x 3 x 53

Step 4: Therefore, the least common multiple of 106 and 108 is 5724.