Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2102 and 2103 the smallest integer that is 4420506 that is divisible by both numbers.
Least Common Multiple (LCM) of 2102 and 2103 is 4420506.
LCM(2102,2103) = 4420506
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 2102 and 2103. First we will calculate the prime factors of 2102 and 2103.
Prime Factorization of 2102
2 | 2102 |
1051 | 1051 |
1 |
Prime factors of 2102 are 2,1051. Prime factorization of 2102 in exponential form is:
2102 = 21×10511
Prime Factorization of 2103
3 | 2103 |
701 | 701 |
1 |
Prime factors of 2103 are 3,701. Prime factorization of 2103 in exponential form is:
2103 = 31×7011
Now multiplying the highest exponent prime factors to calculate the LCM of 2102 and 2103.
LCM(2102,2103) = 21×31×7011×10511
LCM(2102,2103) = 4420506
Factors of 2102
List of positive integer factors of 2102 that divides 2102 without a remainder.
1, 2, 1051, 2102
Factors of 2103
List of positive integer factors of 2103 that divides 2103 without a remainder.
1, 3, 701, 2103
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2102 and 2103, than apply into the LCM equation.
GCF(2102,2103) = 1
LCM(2102,2103) = ( 2102 × 2103) / 1
LCM(2102,2103) = 4420506 / 1
LCM(2102,2103) = 4420506
(i) The LCM of 2103 and 2102 is associative
LCM of 2102 and 2103 = LCM of 2103 and 2102
1. What is the LCM of 2102 and 2103?
Answer: LCM of 2102 and 2103 is 4420506.
2. What are the Factors of 2102?
Answer: Factors of 2102 are 1, 2, 1051, 2102. There are 4 integers that are factors of 2102. The greatest factor of 2102 is 2102.
3. What are the Factors of 2103?
Answer: Factors of 2103 are 1, 3, 701, 2103. There are 4 integers that are factors of 2103. The greatest factor of 2103 is 2103.
4. How to Find the LCM of 2102 and 2103?
Answer:
Least Common Multiple of 2102 and 2103 = 4420506
Step 1: Find the prime factorization of 2102
2102 = 2 x 1051
Step 2: Find the prime factorization of 2103
2103 = 3 x 701
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4420506 = 2 x 3 x 701 x 1051
Step 4: Therefore, the least common multiple of 2102 and 2103 is 4420506.