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 10014 the smallest integer that is 100210098 that is divisible by both numbers.
Least Common Multiple (LCM) of 10007 and 10014 is 100210098.
LCM(10007,10014) = 100210098
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 10014. First we will calculate the prime factors of 10007 and 10014.
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 10014
2 | 10014 |
3 | 5007 |
1669 | 1669 |
1 |
Prime factors of 10014 are 2, 3,1669. Prime factorization of 10014 in exponential form is:
10014 = 21×31×16691
Now multiplying the highest exponent prime factors to calculate the LCM of 10007 and 10014.
LCM(10007,10014) = 21×31×16691×100071
LCM(10007,10014) = 100210098
Factors of 10007
List of positive integer factors of 10007 that divides 10007 without a remainder.
1, 10007
Factors of 10014
List of positive integer factors of 10014 that divides 10014 without a remainder.
1, 2, 3, 6, 1669, 3338, 5007, 10014
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10007 and 10014, than apply into the LCM equation.
GCF(10007,10014) = 1
LCM(10007,10014) = ( 10007 × 10014) / 1
LCM(10007,10014) = 100210098 / 1
LCM(10007,10014) = 100210098
(i) The LCM of 10014 and 10007 is associative
LCM of 10007 and 10014 = LCM of 10014 and 10007
1. What is the LCM of 10007 and 10014?
Answer: LCM of 10007 and 10014 is 100210098.
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 10014?
Answer: Factors of 10014 are 1, 2, 3, 6, 1669, 3338, 5007, 10014. There are 8 integers that are factors of 10014. The greatest factor of 10014 is 10014.
4. How to Find the LCM of 10007 and 10014?
Answer:
Least Common Multiple of 10007 and 10014 = 100210098
Step 1: Find the prime factorization of 10007
10007 = 10007
Step 2: Find the prime factorization of 10014
10014 = 2 x 3 x 1669
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 100210098 = 2 x 3 x 1669 x 10007
Step 4: Therefore, the least common multiple of 10007 and 10014 is 100210098.