Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3005 and 3008 the smallest integer that is 9039040 that is divisible by both numbers.
Least Common Multiple (LCM) of 3005 and 3008 is 9039040.
LCM(3005,3008) = 9039040
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 3005 and 3008. First we will calculate the prime factors of 3005 and 3008.
Prime Factorization of 3005
5 | 3005 |
601 | 601 |
1 |
Prime factors of 3005 are 5,601. Prime factorization of 3005 in exponential form is:
3005 = 51×6011
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 3005 and 3008.
LCM(3005,3008) = 26×51×471×6011
LCM(3005,3008) = 9039040
Factors of 3005
List of positive integer factors of 3005 that divides 3005 without a remainder.
1, 5, 601, 3005
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 3005 and 3008, than apply into the LCM equation.
GCF(3005,3008) = 1
LCM(3005,3008) = ( 3005 × 3008) / 1
LCM(3005,3008) = 9039040 / 1
LCM(3005,3008) = 9039040
(i) The LCM of 3008 and 3005 is associative
LCM of 3005 and 3008 = LCM of 3008 and 3005
1. What is the LCM of 3005 and 3008?
Answer: LCM of 3005 and 3008 is 9039040.
2. What are the Factors of 3005?
Answer: Factors of 3005 are 1, 5, 601, 3005. There are 4 integers that are factors of 3005. The greatest factor of 3005 is 3005.
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 3005 and 3008?
Answer:
Least Common Multiple of 3005 and 3008 = 9039040
Step 1: Find the prime factorization of 3005
3005 = 5 x 601
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 = 9039040 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 47 x 601
Step 4: Therefore, the least common multiple of 3005 and 3008 is 9039040.