Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10007 and 10012 the smallest integer that is 100190084 that is divisible by both numbers.
Least Common Multiple (LCM) of 10007 and 10012 is 100190084.
LCM(10007,10012) = 100190084
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 10007 and 10012. First we will calculate the prime factors of 10007 and 10012.
Prime Factorization of 10007
10007 | 10007 |
1 |
Prime factors of 10007 are 10007. Prime factorization of 10007 in exponential form is:
10007 = 100071
Prime Factorization of 10012
2 | 10012 |
2 | 5006 |
2503 | 2503 |
1 |
Prime factors of 10012 are 2,2503. Prime factorization of 10012 in exponential form is:
10012 = 22×25031
Now multiplying the highest exponent prime factors to calculate the LCM of 10007 and 10012.
LCM(10007,10012) = 22×25031×100071
LCM(10007,10012) = 100190084
Factors of 10007
List of positive integer factors of 10007 that divides 10007 without a remainder.
1, 10007
Factors of 10012
List of positive integer factors of 10012 that divides 10012 without a remainder.
1, 2, 4, 2503, 5006, 10012
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10007 and 10012, than apply into the LCM equation.
GCF(10007,10012) = 1
LCM(10007,10012) = ( 10007 × 10012) / 1
LCM(10007,10012) = 100190084 / 1
LCM(10007,10012) = 100190084
(i) The LCM of 10012 and 10007 is associative
LCM of 10007 and 10012 = LCM of 10012 and 10007
1. What is the LCM of 10007 and 10012?
Answer: LCM of 10007 and 10012 is 100190084.
2. What are the Factors of 10007?
Answer: Factors of 10007 are 1, 10007. There are 2 integers that are factors of 10007. The greatest factor of 10007 is 10007.
3. What are the Factors of 10012?
Answer: Factors of 10012 are 1, 2, 4, 2503, 5006, 10012. There are 6 integers that are factors of 10012. The greatest factor of 10012 is 10012.
4. How to Find the LCM of 10007 and 10012?
Answer:
Least Common Multiple of 10007 and 10012 = 100190084
Step 1: Find the prime factorization of 10007
10007 = 10007
Step 2: Find the prime factorization of 10012
10012 = 2 x 2 x 2503
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 100190084 = 2 x 2 x 2503 x 10007
Step 4: Therefore, the least common multiple of 10007 and 10012 is 100190084.