Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10002 and 10003 the smallest integer that is 100050006 that is divisible by both numbers.
Least Common Multiple (LCM) of 10002 and 10003 is 100050006.
LCM(10002,10003) = 100050006
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 10002 and 10003. First we will calculate the prime factors of 10002 and 10003.
Prime Factorization of 10002
2 | 10002 |
3 | 5001 |
1667 | 1667 |
1 |
Prime factors of 10002 are 2, 3,1667. Prime factorization of 10002 in exponential form is:
10002 = 21×31×16671
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
Now multiplying the highest exponent prime factors to calculate the LCM of 10002 and 10003.
LCM(10002,10003) = 21×31×71×14291×16671
LCM(10002,10003) = 100050006
Factors of 10002
List of positive integer factors of 10002 that divides 10002 without a remainder.
1, 2, 3, 6, 1667, 3334, 5001, 10002
Factors of 10003
List of positive integer factors of 10003 that divides 10003 without a remainder.
1, 7, 1429, 10003
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10002 and 10003, than apply into the LCM equation.
GCF(10002,10003) = 1
LCM(10002,10003) = ( 10002 × 10003) / 1
LCM(10002,10003) = 100050006 / 1
LCM(10002,10003) = 100050006
(i) The LCM of 10003 and 10002 is associative
LCM of 10002 and 10003 = LCM of 10003 and 10002
1. What is the LCM of 10002 and 10003?
Answer: LCM of 10002 and 10003 is 100050006.
2. What are the Factors of 10002?
Answer: Factors of 10002 are 1, 2, 3, 6, 1667, 3334, 5001, 10002. There are 8 integers that are factors of 10002. The greatest factor of 10002 is 10002.
3. 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.
4. How to Find the LCM of 10002 and 10003?
Answer:
Least Common Multiple of 10002 and 10003 = 100050006
Step 1: Find the prime factorization of 10002
10002 = 2 x 3 x 1667
Step 2: Find the prime factorization of 10003
10003 = 7 x 1429
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 100050006 = 2 x 3 x 7 x 1429 x 1667
Step 4: Therefore, the least common multiple of 10002 and 10003 is 100050006.