Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10006 and 10011 the smallest integer that is 100170066 that is divisible by both numbers.
Least Common Multiple (LCM) of 10006 and 10011 is 100170066.
LCM(10006,10011) = 100170066
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 10006 and 10011. First we will calculate the prime factors of 10006 and 10011.
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
Prime Factorization of 10011
3 | 10011 |
47 | 3337 |
71 | 71 |
1 |
Prime factors of 10011 are 3, 47,71. Prime factorization of 10011 in exponential form is:
10011 = 31×471×711
Now multiplying the highest exponent prime factors to calculate the LCM of 10006 and 10011.
LCM(10006,10011) = 21×31×471×711×50031
LCM(10006,10011) = 100170066
Factors of 10006
List of positive integer factors of 10006 that divides 10006 without a remainder.
1, 2, 5003, 10006
Factors of 10011
List of positive integer factors of 10011 that divides 10011 without a remainder.
1, 3, 47, 71, 141, 213, 3337, 10011
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10006 and 10011, than apply into the LCM equation.
GCF(10006,10011) = 1
LCM(10006,10011) = ( 10006 × 10011) / 1
LCM(10006,10011) = 100170066 / 1
LCM(10006,10011) = 100170066
(i) The LCM of 10011 and 10006 is associative
LCM of 10006 and 10011 = LCM of 10011 and 10006
1. What is the LCM of 10006 and 10011?
Answer: LCM of 10006 and 10011 is 100170066.
2. 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.
3. What are the Factors of 10011?
Answer: Factors of 10011 are 1, 3, 47, 71, 141, 213, 3337, 10011. There are 8 integers that are factors of 10011. The greatest factor of 10011 is 10011.
4. How to Find the LCM of 10006 and 10011?
Answer:
Least Common Multiple of 10006 and 10011 = 100170066
Step 1: Find the prime factorization of 10006
10006 = 2 x 5003
Step 2: Find the prime factorization of 10011
10011 = 3 x 47 x 71
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 100170066 = 2 x 3 x 47 x 71 x 5003
Step 4: Therefore, the least common multiple of 10006 and 10011 is 100170066.