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 2107 the smallest integer that is 4437342 that is divisible by both numbers.
Least Common Multiple (LCM) of 2106 and 2107 is 4437342.
LCM(2106,2107) = 4437342
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 2107. First we will calculate the prime factors of 2106 and 2107.
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 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
Now multiplying the highest exponent prime factors to calculate the LCM of 2106 and 2107.
LCM(2106,2107) = 21×34×72×131×431
LCM(2106,2107) = 4437342
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 2107
List of positive integer factors of 2107 that divides 2107 without a remainder.
1, 7, 43, 49, 301, 2107
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2106 and 2107, than apply into the LCM equation.
GCF(2106,2107) = 1
LCM(2106,2107) = ( 2106 × 2107) / 1
LCM(2106,2107) = 4437342 / 1
LCM(2106,2107) = 4437342
(i) The LCM of 2107 and 2106 is associative
LCM of 2106 and 2107 = LCM of 2107 and 2106
1. What is the LCM of 2106 and 2107?
Answer: LCM of 2106 and 2107 is 4437342.
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 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.
4. How to Find the LCM of 2106 and 2107?
Answer:
Least Common Multiple of 2106 and 2107 = 4437342
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 2107
2107 = 7 x 7 x 43
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4437342 = 2 x 3 x 3 x 3 x 3 x 7 x 7 x 13 x 43
Step 4: Therefore, the least common multiple of 2106 and 2107 is 4437342.