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 4107 the smallest integer that is 16846914 that is divisible by both numbers.
Least Common Multiple (LCM) of 4102 and 4107 is 16846914.
LCM(4102,4107) = 16846914
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 4107. First we will calculate the prime factors of 4102 and 4107.
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 4107
3 | 4107 |
37 | 1369 |
37 | 37 |
1 |
Prime factors of 4107 are 3,37. Prime factorization of 4107 in exponential form is:
4107 = 31×372
Now multiplying the highest exponent prime factors to calculate the LCM of 4102 and 4107.
LCM(4102,4107) = 21×31×71×372×2931
LCM(4102,4107) = 16846914
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 4107
List of positive integer factors of 4107 that divides 4107 without a remainder.
1, 3, 37, 111, 1369, 4107
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4102 and 4107, than apply into the LCM equation.
GCF(4102,4107) = 1
LCM(4102,4107) = ( 4102 × 4107) / 1
LCM(4102,4107) = 16846914 / 1
LCM(4102,4107) = 16846914
(i) The LCM of 4107 and 4102 is associative
LCM of 4102 and 4107 = LCM of 4107 and 4102
1. What is the LCM of 4102 and 4107?
Answer: LCM of 4102 and 4107 is 16846914.
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 4107?
Answer: Factors of 4107 are 1, 3, 37, 111, 1369, 4107. There are 6 integers that are factors of 4107. The greatest factor of 4107 is 4107.
4. How to Find the LCM of 4102 and 4107?
Answer:
Least Common Multiple of 4102 and 4107 = 16846914
Step 1: Find the prime factorization of 4102
4102 = 2 x 7 x 293
Step 2: Find the prime factorization of 4107
4107 = 3 x 37 x 37
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 16846914 = 2 x 3 x 7 x 37 x 37 x 293
Step 4: Therefore, the least common multiple of 4102 and 4107 is 16846914.