Least Common Multiple of 2107 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 2107 and 2112 the smallest integer that is 4449984 that is divisible by both numbers.

Least Common Multiple (LCM) of 2107 and 2112 is 4449984.

LCM(2107,2112) = 4449984

LCM of 2107 and 2112

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

LCM of:
and

Least Common Multiple of 2107 and 2112

LCM of 2107 and 2112 is 4449984

Least common multiple can be found by multiplying the highest exponent prime factors of 2107 and 2112. First we will calculate the prime factors of 2107 and 2112.

Prime Factorization of 2107


7 2107
7 301
43 43
1

Prime factors of 2107 are 7,43. Prime factorization of 2107 in exponential form is:

2107 = 72×431

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 2107 and 2112.

LCM(2107,2112) = 26×31×72×111×431
LCM(2107,2112) = 4449984

Factors of 2107

List of positive integer factors of 2107 that divides 2107 without a remainder.

1, 7, 43, 49, 301, 2107

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 2107 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 2107 and 2112, than apply into the LCM equation.

GCF(2107,2112) = 1
LCM(2107,2112) = ( 2107 × 2112) / 1
LCM(2107,2112) = 4449984 / 1
LCM(2107,2112) = 4449984

Properties of LCM 2107 and 2112

(i) The LCM of 2112 and 2107 is associative

LCM of 2107 and 2112 = LCM of 2112 and 2107

Related Least Common Multiples of 2107

Related Least Common Multiples of 2112

Frequently Asked Questions on LCM of 2107 and 2112

1. What is the LCM of 2107 and 2112?

Answer: LCM of 2107 and 2112 is 4449984.

2. What are the Factors of 2107?

Answer: Factors of 2107 are 1, 7, 43, 49, 301, 2107. There are 6 integers that are factors of 2107. The greatest factor of 2107 is 2107.

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 2107 and 2112?

Answer:

Least Common Multiple of 2107 and 2112 = 4449984

Step 1: Find the prime factorization of 2107

2107 = 7 x 7 x 43

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 = 4449984 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 7 x 11 x 43

Step 4: Therefore, the least common multiple of 2107 and 2112 is 4449984.