Least Common Multiple of 3003 and 3007
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3003 and 3007 the smallest integer that is 9030021 that is divisible by both numbers.
Least Common Multiple (LCM) of 3003 and 3007 is 9030021.
LCM(3003,3007) = 9030021
LCM of 3003 and 3007
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 3003 and 3007 by Prime method
- Least Common Multiple of 3003 and 3007 with GCF Formula
LCM of 3003 and 3007 is 9030021
Least common multiple can be found by multiplying the highest exponent prime factors of 3003 and 3007. First we will calculate the prime factors of 3003 and 3007.
Prime Factorization of 3003
| 3 | 3003 |
| 7 | 1001 |
| 11 | 143 |
| 13 | 13 |
| 1 |
Prime factors of 3003 are 3, 7, 11,13. Prime factorization of 3003 in exponential form is:
3003 = 31×71×111×131
Prime Factorization of 3007
| 31 | 3007 |
| 97 | 97 |
| 1 |
Prime factors of 3007 are 31,97. Prime factorization of 3007 in exponential form is:
3007 = 311×971
Now multiplying the highest exponent prime factors to calculate the LCM of 3003 and 3007.
LCM(3003,3007) = 31×71×111×131×311×971
LCM(3003,3007) = 9030021
Factors of 3003
List of positive integer factors of 3003 that divides 3003 without a remainder.
1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003
Factors of 3007
List of positive integer factors of 3007 that divides 3007 without a remainder.
1, 31, 97, 3007
Least Common Multiple of 3003 and 3007 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3003 and 3007, than apply into the LCM equation.
GCF(3003,3007) = 1
LCM(3003,3007) = ( 3003 × 3007) / 1
LCM(3003,3007) = 9030021 / 1
LCM(3003,3007) = 9030021
Properties of LCM 3003 and 3007
(i) The LCM of 3007 and 3003 is associative
LCM of 3003 and 3007 = LCM of 3007 and 3003
Related Least Common Multiples of 3003
Related Least Common Multiples of 3007
Frequently Asked Questions on LCM of 3003 and 3007
1. What is the LCM of 3003 and 3007?
Answer: LCM of 3003 and 3007 is 9030021.
2. What are the Factors of 3003?
Answer: Factors of 3003 are 1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003. There are 16 integers that are factors of 3003. The greatest factor of 3003 is 3003.
3. What are the Factors of 3007?
Answer: Factors of 3007 are 1, 31, 97, 3007. There are 4 integers that are factors of 3007. The greatest factor of 3007 is 3007.
4. How to Find the LCM of 3003 and 3007?
Answer:
Least Common Multiple of 3003 and 3007 = 9030021
Step 1: Find the prime factorization of 3003
3003 = 3 x 7 x 11 x 13
Step 2: Find the prime factorization of 3007
3007 = 31 x 97
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 9030021 = 3 x 7 x 11 x 13 x 31 x 97
Step 4: Therefore, the least common multiple of 3003 and 3007 is 9030021.
