Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 5005 and 5007 the smallest integer that is 25060035 that is divisible by both numbers.
Least Common Multiple (LCM) of 5005 and 5007 is 25060035.
LCM(5005,5007) = 25060035
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 5005 and 5007. First we will calculate the prime factors of 5005 and 5007.
Prime Factorization of 5005
5 | 5005 |
7 | 1001 |
11 | 143 |
13 | 13 |
1 |
Prime factors of 5005 are 5, 7, 11,13. Prime factorization of 5005 in exponential form is:
5005 = 51×71×111×131
Prime Factorization of 5007
3 | 5007 |
1669 | 1669 |
1 |
Prime factors of 5007 are 3,1669. Prime factorization of 5007 in exponential form is:
5007 = 31×16691
Now multiplying the highest exponent prime factors to calculate the LCM of 5005 and 5007.
LCM(5005,5007) = 31×51×71×111×131×16691
LCM(5005,5007) = 25060035
Factors of 5005
List of positive integer factors of 5005 that divides 5005 without a remainder.
1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005
Factors of 5007
List of positive integer factors of 5007 that divides 5007 without a remainder.
1, 3, 1669, 5007
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5005 and 5007, than apply into the LCM equation.
GCF(5005,5007) = 1
LCM(5005,5007) = ( 5005 × 5007) / 1
LCM(5005,5007) = 25060035 / 1
LCM(5005,5007) = 25060035
(i) The LCM of 5007 and 5005 is associative
LCM of 5005 and 5007 = LCM of 5007 and 5005
1. What is the LCM of 5005 and 5007?
Answer: LCM of 5005 and 5007 is 25060035.
2. What are the Factors of 5005?
Answer: Factors of 5005 are 1, 5, 7, 11, 13, 35, 55, 65, 77, 91, 143, 385, 455, 715, 1001, 5005. There are 16 integers that are factors of 5005. The greatest factor of 5005 is 5005.
3. What are the Factors of 5007?
Answer: Factors of 5007 are 1, 3, 1669, 5007. There are 4 integers that are factors of 5007. The greatest factor of 5007 is 5007.
4. How to Find the LCM of 5005 and 5007?
Answer:
Least Common Multiple of 5005 and 5007 = 25060035
Step 1: Find the prime factorization of 5005
5005 = 5 x 7 x 11 x 13
Step 2: Find the prime factorization of 5007
5007 = 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 = 25060035 = 3 x 5 x 7 x 11 x 13 x 1669
Step 4: Therefore, the least common multiple of 5005 and 5007 is 25060035.