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 2106 the smallest integer that is 4433130 that is divisible by both numbers.
Least Common Multiple (LCM) of 2105 and 2106 is 4433130.
LCM(2105,2106) = 4433130
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 2105 and 2106. First we will calculate the prime factors of 2105 and 2106.
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 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
Now multiplying the highest exponent prime factors to calculate the LCM of 2105 and 2106.
LCM(2105,2106) = 21×34×51×131×4211
LCM(2105,2106) = 4433130
Factors of 2105
List of positive integer factors of 2105 that divides 2105 without a remainder.
1, 5, 421, 2105
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
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2105 and 2106, than apply into the LCM equation.
GCF(2105,2106) = 1
LCM(2105,2106) = ( 2105 × 2106) / 1
LCM(2105,2106) = 4433130 / 1
LCM(2105,2106) = 4433130
(i) The LCM of 2106 and 2105 is associative
LCM of 2105 and 2106 = LCM of 2106 and 2105
1. What is the LCM of 2105 and 2106?
Answer: LCM of 2105 and 2106 is 4433130.
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 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.
4. How to Find the LCM of 2105 and 2106?
Answer:
Least Common Multiple of 2105 and 2106 = 4433130
Step 1: Find the prime factorization of 2105
2105 = 5 x 421
Step 2: Find the prime factorization of 2106
2106 = 2 x 3 x 3 x 3 x 3 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4433130 = 2 x 3 x 3 x 3 x 3 x 5 x 13 x 421
Step 4: Therefore, the least common multiple of 2105 and 2106 is 4433130.