Least Common Multiple of 2106 and 2109

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2106 and 2109 the smallest integer that is 1480518 that is divisible by both numbers.

Least Common Multiple (LCM) of 2106 and 2109 is 1480518.

LCM(2106,2109) = 1480518

LCM of 2106 and 2109

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

LCM of:
and

Least Common Multiple of 2106 and 2109

LCM of 2106 and 2109 is 1480518

Least common multiple can be found by multiplying the highest exponent prime factors of 2106 and 2109. First we will calculate the prime factors of 2106 and 2109.

Prime Factorization of 2106


2 2106
3 1053
3 351
3 117
3 39
13 13
1

Prime factors of 2106 are 2, 3,13. Prime factorization of 2106 in exponential form is:

2106 = 21×34×131

Prime Factorization of 2109


3 2109
19 703
37 37
1

Prime factors of 2109 are 3, 19,37. Prime factorization of 2109 in exponential form is:

2109 = 31×191×371

Now multiplying the highest exponent prime factors to calculate the LCM of 2106 and 2109.

LCM(2106,2109) = 21×34×131×191×371
LCM(2106,2109) = 1480518

Factors of 2106

List of positive integer factors of 2106 that divides 2106 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 234, 351, 702, 1053, 2106

Factors of 2109

List of positive integer factors of 2109 that divides 2109 without a remainder.

1, 3, 19, 37, 57, 111, 703, 2109

Least Common Multiple of 2106 and 2109 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2106 and 2109, than apply into the LCM equation.

GCF(2106,2109) = 3
LCM(2106,2109) = ( 2106 × 2109) / 3
LCM(2106,2109) = 4441554 / 3
LCM(2106,2109) = 1480518

Properties of LCM 2106 and 2109

(i) The LCM of 2109 and 2106 is associative

LCM of 2106 and 2109 = LCM of 2109 and 2106

Related Least Common Multiples of 2106

Related Least Common Multiples of 2109

Frequently Asked Questions on LCM of 2106 and 2109

1. What is the LCM of 2106 and 2109?

Answer: LCM of 2106 and 2109 is 1480518.

2. What are the Factors of 2106?

Answer: Factors of 2106 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 234, 351, 702, 1053, 2106. There are 20 integers that are factors of 2106. The greatest factor of 2106 is 2106.

3. What are the Factors of 2109?

Answer: Factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109. There are 8 integers that are factors of 2109. The greatest factor of 2109 is 2109.

4. How to Find the LCM of 2106 and 2109?

Answer:

Least Common Multiple of 2106 and 2109 = 1480518

Step 1: Find the prime factorization of 2106

2106 = 2 x 3 x 3 x 3 x 3 x 13

Step 2: Find the prime factorization of 2109

2109 = 3 x 19 x 37

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

LCM = 1480518 = 2 x 3 x 3 x 3 x 3 x 13 x 19 x 37

Step 4: Therefore, the least common multiple of 2106 and 2109 is 1480518.