Least Common Multiple of 3105 and 3112

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3105 and 3112 the smallest integer that is 9662760 that is divisible by both numbers.

Least Common Multiple (LCM) of 3105 and 3112 is 9662760.

LCM(3105,3112) = 9662760

LCM of 3105 and 3112

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

LCM of:
and

Least Common Multiple of 3105 and 3112

LCM of 3105 and 3112 is 9662760

Least common multiple can be found by multiplying the highest exponent prime factors of 3105 and 3112. First we will calculate the prime factors of 3105 and 3112.

Prime Factorization of 3105


3 3105
3 1035
3 345
5 115
23 23
1

Prime factors of 3105 are 3, 5,23. Prime factorization of 3105 in exponential form is:

3105 = 33×51×231

Prime Factorization of 3112


2 3112
2 1556
2 778
389 389
1

Prime factors of 3112 are 2,389. Prime factorization of 3112 in exponential form is:

3112 = 23×3891

Now multiplying the highest exponent prime factors to calculate the LCM of 3105 and 3112.

LCM(3105,3112) = 23×33×51×231×3891
LCM(3105,3112) = 9662760

Factors of 3105

List of positive integer factors of 3105 that divides 3105 without a remainder.

1, 3, 5, 9, 15, 23, 27, 45, 69, 115, 135, 207, 345, 621, 1035, 3105

Factors of 3112

List of positive integer factors of 3112 that divides 3112 without a remainder.

1, 2, 4, 8, 389, 778, 1556, 3112

Least Common Multiple of 3105 and 3112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3105 and 3112, than apply into the LCM equation.

GCF(3105,3112) = 1
LCM(3105,3112) = ( 3105 × 3112) / 1
LCM(3105,3112) = 9662760 / 1
LCM(3105,3112) = 9662760

Properties of LCM 3105 and 3112

(i) The LCM of 3112 and 3105 is associative

LCM of 3105 and 3112 = LCM of 3112 and 3105

Related Least Common Multiples of 3105

Related Least Common Multiples of 3112

Frequently Asked Questions on LCM of 3105 and 3112

1. What is the LCM of 3105 and 3112?

Answer: LCM of 3105 and 3112 is 9662760.

2. What are the Factors of 3105?

Answer: Factors of 3105 are 1, 3, 5, 9, 15, 23, 27, 45, 69, 115, 135, 207, 345, 621, 1035, 3105. There are 16 integers that are factors of 3105. The greatest factor of 3105 is 3105.

3. What are the Factors of 3112?

Answer: Factors of 3112 are 1, 2, 4, 8, 389, 778, 1556, 3112. There are 8 integers that are factors of 3112. The greatest factor of 3112 is 3112.

4. How to Find the LCM of 3105 and 3112?

Answer:

Least Common Multiple of 3105 and 3112 = 9662760

Step 1: Find the prime factorization of 3105

3105 = 3 x 3 x 3 x 5 x 23

Step 2: Find the prime factorization of 3112

3112 = 2 x 2 x 2 x 389

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

LCM = 9662760 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 23 x 389

Step 4: Therefore, the least common multiple of 3105 and 3112 is 9662760.