Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 4097 and 4102 the smallest integer that is 16805894 that is divisible by both numbers.
Least Common Multiple (LCM) of 4097 and 4102 is 16805894.
LCM(4097,4102) = 16805894
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 4097 and 4102. First we will calculate the prime factors of 4097 and 4102.
Prime Factorization of 4097
17 | 4097 |
241 | 241 |
1 |
Prime factors of 4097 are 17,241. Prime factorization of 4097 in exponential form is:
4097 = 171×2411
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
Now multiplying the highest exponent prime factors to calculate the LCM of 4097 and 4102.
LCM(4097,4102) = 21×71×171×2411×2931
LCM(4097,4102) = 16805894
Factors of 4097
List of positive integer factors of 4097 that divides 4097 without a remainder.
1, 17, 241, 4097
Factors of 4102
List of positive integer factors of 4102 that divides 4102 without a remainder.
1, 2, 7, 14, 293, 586, 2051, 4102
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4097 and 4102, than apply into the LCM equation.
GCF(4097,4102) = 1
LCM(4097,4102) = ( 4097 × 4102) / 1
LCM(4097,4102) = 16805894 / 1
LCM(4097,4102) = 16805894
(i) The LCM of 4102 and 4097 is associative
LCM of 4097 and 4102 = LCM of 4102 and 4097
1. What is the LCM of 4097 and 4102?
Answer: LCM of 4097 and 4102 is 16805894.
2. What are the Factors of 4097?
Answer: Factors of 4097 are 1, 17, 241, 4097. There are 4 integers that are factors of 4097. The greatest factor of 4097 is 4097.
3. 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.
4. How to Find the LCM of 4097 and 4102?
Answer:
Least Common Multiple of 4097 and 4102 = 16805894
Step 1: Find the prime factorization of 4097
4097 = 17 x 241
Step 2: Find the prime factorization of 4102
4102 = 2 x 7 x 293
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 16805894 = 2 x 7 x 17 x 241 x 293
Step 4: Therefore, the least common multiple of 4097 and 4102 is 16805894.