Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 4102 and 4109 the smallest integer that is 2407874 that is divisible by both numbers.
Least Common Multiple (LCM) of 4102 and 4109 is 2407874.
LCM(4102,4109) = 2407874
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 4102 and 4109. First we will calculate the prime factors of 4102 and 4109.
Prime Factorization of 4102
2 | 4102 |
7 | 2051 |
293 | 293 |
1 |
Prime factors of 4102 are 2, 7,293. Prime factorization of 4102 in exponential form is:
4102 = 21×71×2931
Prime Factorization of 4109
7 | 4109 |
587 | 587 |
1 |
Prime factors of 4109 are 7,587. Prime factorization of 4109 in exponential form is:
4109 = 71×5871
Now multiplying the highest exponent prime factors to calculate the LCM of 4102 and 4109.
LCM(4102,4109) = 21×71×2931×5871
LCM(4102,4109) = 2407874
Factors of 4102
List of positive integer factors of 4102 that divides 4102 without a remainder.
1, 2, 7, 14, 293, 586, 2051, 4102
Factors of 4109
List of positive integer factors of 4109 that divides 4109 without a remainder.
1, 7, 587, 4109
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4102 and 4109, than apply into the LCM equation.
GCF(4102,4109) = 7
LCM(4102,4109) = ( 4102 × 4109) / 7
LCM(4102,4109) = 16855118 / 7
LCM(4102,4109) = 2407874
(i) The LCM of 4109 and 4102 is associative
LCM of 4102 and 4109 = LCM of 4109 and 4102
1. What is the LCM of 4102 and 4109?
Answer: LCM of 4102 and 4109 is 2407874.
2. What are the Factors of 4102?
Answer: Factors of 4102 are 1, 2, 7, 14, 293, 586, 2051, 4102. There are 8 integers that are factors of 4102. The greatest factor of 4102 is 4102.
3. What are the Factors of 4109?
Answer: Factors of 4109 are 1, 7, 587, 4109. There are 4 integers that are factors of 4109. The greatest factor of 4109 is 4109.
4. How to Find the LCM of 4102 and 4109?
Answer:
Least Common Multiple of 4102 and 4109 = 2407874
Step 1: Find the prime factorization of 4102
4102 = 2 x 7 x 293
Step 2: Find the prime factorization of 4109
4109 = 7 x 587
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2407874 = 2 x 7 x 293 x 587
Step 4: Therefore, the least common multiple of 4102 and 4109 is 2407874.