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 3008 the smallest integer that is 9033024 that is divisible by both numbers.
Least Common Multiple (LCM) of 3003 and 3008 is 9033024.
LCM(3003,3008) = 9033024
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 3003 and 3008. First we will calculate the prime factors of 3003 and 3008.
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 3008
2 | 3008 |
2 | 1504 |
2 | 752 |
2 | 376 |
2 | 188 |
2 | 94 |
47 | 47 |
1 |
Prime factors of 3008 are 2,47. Prime factorization of 3008 in exponential form is:
3008 = 26×471
Now multiplying the highest exponent prime factors to calculate the LCM of 3003 and 3008.
LCM(3003,3008) = 26×31×71×111×131×471
LCM(3003,3008) = 9033024
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 3008
List of positive integer factors of 3008 that divides 3008 without a remainder.
1, 2, 4, 8, 16, 32, 47, 64, 94, 188, 376, 752, 1504, 3008
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3003 and 3008, than apply into the LCM equation.
GCF(3003,3008) = 1
LCM(3003,3008) = ( 3003 × 3008) / 1
LCM(3003,3008) = 9033024 / 1
LCM(3003,3008) = 9033024
(i) The LCM of 3008 and 3003 is associative
LCM of 3003 and 3008 = LCM of 3008 and 3003
1. What is the LCM of 3003 and 3008?
Answer: LCM of 3003 and 3008 is 9033024.
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 3008?
Answer: Factors of 3008 are 1, 2, 4, 8, 16, 32, 47, 64, 94, 188, 376, 752, 1504, 3008. There are 14 integers that are factors of 3008. The greatest factor of 3008 is 3008.
4. How to Find the LCM of 3003 and 3008?
Answer:
Least Common Multiple of 3003 and 3008 = 9033024
Step 1: Find the prime factorization of 3003
3003 = 3 x 7 x 11 x 13
Step 2: Find the prime factorization of 3008
3008 = 2 x 2 x 2 x 2 x 2 x 2 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 9033024 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 11 x 13 x 47
Step 4: Therefore, the least common multiple of 3003 and 3008 is 9033024.