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 3012 the smallest integer that is 9051060 that is divisible by both numbers.
Least Common Multiple (LCM) of 3005 and 3012 is 9051060.
LCM(3005,3012) = 9051060
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 3012. First we will calculate the prime factors of 3005 and 3012.
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 3012
2 | 3012 |
2 | 1506 |
3 | 753 |
251 | 251 |
1 |
Prime factors of 3012 are 2, 3,251. Prime factorization of 3012 in exponential form is:
3012 = 22×31×2511
Now multiplying the highest exponent prime factors to calculate the LCM of 3005 and 3012.
LCM(3005,3012) = 22×31×51×2511×6011
LCM(3005,3012) = 9051060
Factors of 3005
List of positive integer factors of 3005 that divides 3005 without a remainder.
1, 5, 601, 3005
Factors of 3012
List of positive integer factors of 3012 that divides 3012 without a remainder.
1, 2, 3, 4, 6, 12, 251, 502, 753, 1004, 1506, 3012
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3005 and 3012, than apply into the LCM equation.
GCF(3005,3012) = 1
LCM(3005,3012) = ( 3005 × 3012) / 1
LCM(3005,3012) = 9051060 / 1
LCM(3005,3012) = 9051060
(i) The LCM of 3012 and 3005 is associative
LCM of 3005 and 3012 = LCM of 3012 and 3005
1. What is the LCM of 3005 and 3012?
Answer: LCM of 3005 and 3012 is 9051060.
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 3012?
Answer: Factors of 3012 are 1, 2, 3, 4, 6, 12, 251, 502, 753, 1004, 1506, 3012. There are 12 integers that are factors of 3012. The greatest factor of 3012 is 3012.
4. How to Find the LCM of 3005 and 3012?
Answer:
Least Common Multiple of 3005 and 3012 = 9051060
Step 1: Find the prime factorization of 3005
3005 = 5 x 601
Step 2: Find the prime factorization of 3012
3012 = 2 x 2 x 3 x 251
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 9051060 = 2 x 2 x 3 x 5 x 251 x 601
Step 4: Therefore, the least common multiple of 3005 and 3012 is 9051060.