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
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
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
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
(i) The LCM of 2109 and 2106 is associative
LCM of 2106 and 2109 = LCM of 2109 and 2106
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.