Least Common Multiple of 2105 and 2112

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2105 and 2112 the smallest integer that is 4445760 that is divisible by both numbers.

Least Common Multiple (LCM) of 2105 and 2112 is 4445760.

LCM(2105,2112) = 4445760

LCM of 2105 and 2112

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

LCM of:
and

Least Common Multiple of 2105 and 2112

LCM of 2105 and 2112 is 4445760

Least common multiple can be found by multiplying the highest exponent prime factors of 2105 and 2112. First we will calculate the prime factors of 2105 and 2112.

Prime Factorization of 2105


5 2105
421 421
1

Prime factors of 2105 are 5,421. Prime factorization of 2105 in exponential form is:

2105 = 51×4211

Prime Factorization of 2112


2 2112
2 1056
2 528
2 264
2 132
2 66
3 33
11 11
1

Prime factors of 2112 are 2, 3,11. Prime factorization of 2112 in exponential form is:

2112 = 26×31×111

Now multiplying the highest exponent prime factors to calculate the LCM of 2105 and 2112.

LCM(2105,2112) = 26×31×51×111×4211
LCM(2105,2112) = 4445760

Factors of 2105

List of positive integer factors of 2105 that divides 2105 without a remainder.

1, 5, 421, 2105

Factors of 2112

List of positive integer factors of 2112 that divides 2112 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 132, 176, 192, 264, 352, 528, 704, 1056, 2112

Least Common Multiple of 2105 and 2112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2105 and 2112, than apply into the LCM equation.

GCF(2105,2112) = 1
LCM(2105,2112) = ( 2105 × 2112) / 1
LCM(2105,2112) = 4445760 / 1
LCM(2105,2112) = 4445760

Properties of LCM 2105 and 2112

(i) The LCM of 2112 and 2105 is associative

LCM of 2105 and 2112 = LCM of 2112 and 2105

Related Least Common Multiples of 2105

Related Least Common Multiples of 2112

Frequently Asked Questions on LCM of 2105 and 2112

1. What is the LCM of 2105 and 2112?

Answer: LCM of 2105 and 2112 is 4445760.

2. What are the Factors of 2105?

Answer: Factors of 2105 are 1, 5, 421, 2105. There are 4 integers that are factors of 2105. The greatest factor of 2105 is 2105.

3. What are the Factors of 2112?

Answer: Factors of 2112 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 132, 176, 192, 264, 352, 528, 704, 1056, 2112. There are 28 integers that are factors of 2112. The greatest factor of 2112 is 2112.

4. How to Find the LCM of 2105 and 2112?

Answer:

Least Common Multiple of 2105 and 2112 = 4445760

Step 1: Find the prime factorization of 2105

2105 = 5 x 421

Step 2: Find the prime factorization of 2112

2112 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 11

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

LCM = 4445760 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 11 x 421

Step 4: Therefore, the least common multiple of 2105 and 2112 is 4445760.