Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10003 and 10006 the smallest integer that is 100090018 that is divisible by both numbers.
Least Common Multiple (LCM) of 10003 and 10006 is 100090018.
LCM(10003,10006) = 100090018
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 10003 and 10006. First we will calculate the prime factors of 10003 and 10006.
Prime Factorization of 10003
7 | 10003 |
1429 | 1429 |
1 |
Prime factors of 10003 are 7,1429. Prime factorization of 10003 in exponential form is:
10003 = 71×14291
Prime Factorization of 10006
2 | 10006 |
5003 | 5003 |
1 |
Prime factors of 10006 are 2,5003. Prime factorization of 10006 in exponential form is:
10006 = 21×50031
Now multiplying the highest exponent prime factors to calculate the LCM of 10003 and 10006.
LCM(10003,10006) = 21×71×14291×50031
LCM(10003,10006) = 100090018
Factors of 10003
List of positive integer factors of 10003 that divides 10003 without a remainder.
1, 7, 1429, 10003
Factors of 10006
List of positive integer factors of 10006 that divides 10006 without a remainder.
1, 2, 5003, 10006
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10003 and 10006, than apply into the LCM equation.
GCF(10003,10006) = 1
LCM(10003,10006) = ( 10003 × 10006) / 1
LCM(10003,10006) = 100090018 / 1
LCM(10003,10006) = 100090018
(i) The LCM of 10006 and 10003 is associative
LCM of 10003 and 10006 = LCM of 10006 and 10003
1. What is the LCM of 10003 and 10006?
Answer: LCM of 10003 and 10006 is 100090018.
2. What are the Factors of 10003?
Answer: Factors of 10003 are 1, 7, 1429, 10003. There are 4 integers that are factors of 10003. The greatest factor of 10003 is 10003.
3. What are the Factors of 10006?
Answer: Factors of 10006 are 1, 2, 5003, 10006. There are 4 integers that are factors of 10006. The greatest factor of 10006 is 10006.
4. How to Find the LCM of 10003 and 10006?
Answer:
Least Common Multiple of 10003 and 10006 = 100090018
Step 1: Find the prime factorization of 10003
10003 = 7 x 1429
Step 2: Find the prime factorization of 10006
10006 = 2 x 5003
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 100090018 = 2 x 7 x 1429 x 5003
Step 4: Therefore, the least common multiple of 10003 and 10006 is 100090018.