Least Common Multiple of 10005 and 10007
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10005 and 10007 the smallest integer that is 100120035 that is divisible by both numbers.
Least Common Multiple (LCM) of 10005 and 10007 is 100120035.
LCM(10005,10007) = 100120035
LCM of 10005 and 10007
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 10005 and 10007 by Prime method
- Least Common Multiple of 10005 and 10007 with GCF Formula
LCM of 10005 and 10007 is 100120035
Least common multiple can be found by multiplying the highest exponent prime factors of 10005 and 10007. First we will calculate the prime factors of 10005 and 10007.
Prime Factorization of 10005
| 3 | 10005 |
| 5 | 3335 |
| 23 | 667 |
| 29 | 29 |
| 1 |
Prime factors of 10005 are 3, 5, 23,29. Prime factorization of 10005 in exponential form is:
10005 = 31×51×231×291
Prime Factorization of 10007
| 10007 | 10007 |
| 1 |
Prime factors of 10007 are 10007. Prime factorization of 10007 in exponential form is:
10007 = 100071
Now multiplying the highest exponent prime factors to calculate the LCM of 10005 and 10007.
LCM(10005,10007) = 31×51×231×291×100071
LCM(10005,10007) = 100120035
Factors of 10005
List of positive integer factors of 10005 that divides 10005 without a remainder.
1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2001, 3335, 10005
Factors of 10007
List of positive integer factors of 10007 that divides 10007 without a remainder.
1, 10007
Least Common Multiple of 10005 and 10007 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10005 and 10007, than apply into the LCM equation.
GCF(10005,10007) = 1
LCM(10005,10007) = ( 10005 × 10007) / 1
LCM(10005,10007) = 100120035 / 1
LCM(10005,10007) = 100120035
Properties of LCM 10005 and 10007
(i) The LCM of 10007 and 10005 is associative
LCM of 10005 and 10007 = LCM of 10007 and 10005
Related Least Common Multiples of 10005
Related Least Common Multiples of 10007
Frequently Asked Questions on LCM of 10005 and 10007
1. What is the LCM of 10005 and 10007?
Answer: LCM of 10005 and 10007 is 100120035.
2. What are the Factors of 10005?
Answer: Factors of 10005 are 1, 3, 5, 15, 23, 29, 69, 87, 115, 145, 345, 435, 667, 2001, 3335, 10005. There are 16 integers that are factors of 10005. The greatest factor of 10005 is 10005.
3. 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.
4. How to Find the LCM of 10005 and 10007?
Answer:
Least Common Multiple of 10005 and 10007 = 100120035
Step 1: Find the prime factorization of 10005
10005 = 3 x 5 x 23 x 29
Step 2: Find the prime factorization of 10007
10007 = 10007
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 100120035 = 3 x 5 x 23 x 29 x 10007
Step 4: Therefore, the least common multiple of 10005 and 10007 is 100120035.
