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 2113 the smallest integer that is 4447865 that is divisible by both numbers.
Least Common Multiple (LCM) of 2105 and 2113 is 4447865.
LCM(2105,2113) = 4447865
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 2113. First we will calculate the prime factors of 2105 and 2113.
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 2113
2113 | 2113 |
1 |
Prime factors of 2113 are 2113. Prime factorization of 2113 in exponential form is:
2113 = 21131
Now multiplying the highest exponent prime factors to calculate the LCM of 2105 and 2113.
LCM(2105,2113) = 51×4211×21131
LCM(2105,2113) = 4447865
Factors of 2105
List of positive integer factors of 2105 that divides 2105 without a remainder.
1, 5, 421, 2105
Factors of 2113
List of positive integer factors of 2113 that divides 2113 without a remainder.
1, 2113
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2105 and 2113, than apply into the LCM equation.
GCF(2105,2113) = 1
LCM(2105,2113) = ( 2105 × 2113) / 1
LCM(2105,2113) = 4447865 / 1
LCM(2105,2113) = 4447865
(i) The LCM of 2113 and 2105 is associative
LCM of 2105 and 2113 = LCM of 2113 and 2105
1. What is the LCM of 2105 and 2113?
Answer: LCM of 2105 and 2113 is 4447865.
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 2113?
Answer: Factors of 2113 are 1, 2113. There are 2 integers that are factors of 2113. The greatest factor of 2113 is 2113.
4. How to Find the LCM of 2105 and 2113?
Answer:
Least Common Multiple of 2105 and 2113 = 4447865
Step 1: Find the prime factorization of 2105
2105 = 5 x 421
Step 2: Find the prime factorization of 2113
2113 = 2113
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4447865 = 5 x 421 x 2113
Step 4: Therefore, the least common multiple of 2105 and 2113 is 4447865.