Least Common Multiple of 3002 and 3003
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3002 and 3003 the smallest integer that is 9015006 that is divisible by both numbers.
Least Common Multiple (LCM) of 3002 and 3003 is 9015006.
LCM(3002,3003) = 9015006
LCM of 3002 and 3003
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 3002 and 3003 by Prime method
- Least Common Multiple of 3002 and 3003 with GCF Formula
LCM of 3002 and 3003 is 9015006
Least common multiple can be found by multiplying the highest exponent prime factors of 3002 and 3003. First we will calculate the prime factors of 3002 and 3003.
Prime Factorization of 3002
| 2 | 3002 |
| 19 | 1501 |
| 79 | 79 |
| 1 |
Prime factors of 3002 are 2, 19,79. Prime factorization of 3002 in exponential form is:
3002 = 21×191×791
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
Now multiplying the highest exponent prime factors to calculate the LCM of 3002 and 3003.
LCM(3002,3003) = 21×31×71×111×131×191×791
LCM(3002,3003) = 9015006
Factors of 3002
List of positive integer factors of 3002 that divides 3002 without a remainder.
1, 2, 19, 38, 79, 158, 1501, 3002
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
Least Common Multiple of 3002 and 3003 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3002 and 3003, than apply into the LCM equation.
GCF(3002,3003) = 1
LCM(3002,3003) = ( 3002 × 3003) / 1
LCM(3002,3003) = 9015006 / 1
LCM(3002,3003) = 9015006
Properties of LCM 3002 and 3003
(i) The LCM of 3003 and 3002 is associative
LCM of 3002 and 3003 = LCM of 3003 and 3002
Related Least Common Multiples of 3002
Related Least Common Multiples of 3003
Frequently Asked Questions on LCM of 3002 and 3003
1. What is the LCM of 3002 and 3003?
Answer: LCM of 3002 and 3003 is 9015006.
2. What are the Factors of 3002?
Answer: Factors of 3002 are 1, 2, 19, 38, 79, 158, 1501, 3002. There are 8 integers that are factors of 3002. The greatest factor of 3002 is 3002.
3. 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.
4. How to Find the LCM of 3002 and 3003?
Answer:
Least Common Multiple of 3002 and 3003 = 9015006
Step 1: Find the prime factorization of 3002
3002 = 2 x 19 x 79
Step 2: Find the prime factorization of 3003
3003 = 3 x 7 x 11 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 9015006 = 2 x 3 x 7 x 11 x 13 x 19 x 79
Step 4: Therefore, the least common multiple of 3002 and 3003 is 9015006.
