Least Common Multiple of 2007 and 2012
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 2007 and 2012 the smallest integer that is 4038084 that is divisible by both numbers.
Least Common Multiple (LCM) of 2007 and 2012 is 4038084.
LCM(2007,2012) = 4038084
LCM of 2007 and 2012
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2007 and 2012 by Prime method
- Least Common Multiple of 2007 and 2012 with GCF Formula
LCM of 2007 and 2012 is 4038084
Least common multiple can be found by multiplying the highest exponent prime factors of 2007 and 2012. First we will calculate the prime factors of 2007 and 2012.
Prime Factorization of 2007
| 3 | 2007 |
| 3 | 669 |
| 223 | 223 |
| 1 |
Prime factors of 2007 are 3,223. Prime factorization of 2007 in exponential form is:
2007 = 32×2231
Prime Factorization of 2012
| 2 | 2012 |
| 2 | 1006 |
| 503 | 503 |
| 1 |
Prime factors of 2012 are 2,503. Prime factorization of 2012 in exponential form is:
2012 = 22×5031
Now multiplying the highest exponent prime factors to calculate the LCM of 2007 and 2012.
LCM(2007,2012) = 22×32×2231×5031
LCM(2007,2012) = 4038084
Factors of 2007
List of positive integer factors of 2007 that divides 2007 without a remainder.
1, 3, 9, 223, 669, 2007
Factors of 2012
List of positive integer factors of 2012 that divides 2012 without a remainder.
1, 2, 4, 503, 1006, 2012
Least Common Multiple of 2007 and 2012 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2007 and 2012, than apply into the LCM equation.
GCF(2007,2012) = 1
LCM(2007,2012) = ( 2007 × 2012) / 1
LCM(2007,2012) = 4038084 / 1
LCM(2007,2012) = 4038084
Properties of LCM 2007 and 2012
(i) The LCM of 2012 and 2007 is associative
LCM of 2007 and 2012 = LCM of 2012 and 2007
Related Least Common Multiples of 2007
Related Least Common Multiples of 2012
Frequently Asked Questions on LCM of 2007 and 2012
1. What is the LCM of 2007 and 2012?
Answer: LCM of 2007 and 2012 is 4038084.
2. What are the Factors of 2007?
Answer: Factors of 2007 are 1, 3, 9, 223, 669, 2007. There are 6 integers that are factors of 2007. The greatest factor of 2007 is 2007.
3. What are the Factors of 2012?
Answer: Factors of 2012 are 1, 2, 4, 503, 1006, 2012. There are 6 integers that are factors of 2012. The greatest factor of 2012 is 2012.
4. How to Find the LCM of 2007 and 2012?
Answer:
Least Common Multiple of 2007 and 2012 = 4038084
Step 1: Find the prime factorization of 2007
2007 = 3 x 3 x 223
Step 2: Find the prime factorization of 2012
2012 = 2 x 2 x 503
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4038084 = 2 x 2 x 3 x 3 x 223 x 503
Step 4: Therefore, the least common multiple of 2007 and 2012 is 4038084.