Least Common Multiple of 2004 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 2004 and 2012 the smallest integer that is 1008012 that is divisible by both numbers.
Least Common Multiple (LCM) of 2004 and 2012 is 1008012.
LCM(2004,2012) = 1008012
LCM of 2004 and 2012
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2004 and 2012 by Prime method
- Least Common Multiple of 2004 and 2012 with GCF Formula
LCM of 2004 and 2012 is 1008012
Least common multiple can be found by multiplying the highest exponent prime factors of 2004 and 2012. First we will calculate the prime factors of 2004 and 2012.
Prime Factorization of 2004
| 2 | 2004 |
| 2 | 1002 |
| 3 | 501 |
| 167 | 167 |
| 1 |
Prime factors of 2004 are 2, 3,167. Prime factorization of 2004 in exponential form is:
2004 = 22×31×1671
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 2004 and 2012.
LCM(2004,2012) = 22×31×1671×5031
LCM(2004,2012) = 1008012
Factors of 2004
List of positive integer factors of 2004 that divides 2004 without a remainder.
1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004
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 2004 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 2004 and 2012, than apply into the LCM equation.
GCF(2004,2012) = 4
LCM(2004,2012) = ( 2004 × 2012) / 4
LCM(2004,2012) = 4032048 / 4
LCM(2004,2012) = 1008012
Properties of LCM 2004 and 2012
(i) The LCM of 2012 and 2004 is associative
LCM of 2004 and 2012 = LCM of 2012 and 2004
Related Least Common Multiples of 2004
Related Least Common Multiples of 2012
Frequently Asked Questions on LCM of 2004 and 2012
1. What is the LCM of 2004 and 2012?
Answer: LCM of 2004 and 2012 is 1008012.
2. What are the Factors of 2004?
Answer: Factors of 2004 are 1, 2, 3, 4, 6, 12, 167, 334, 501, 668, 1002, 2004. There are 12 integers that are factors of 2004. The greatest factor of 2004 is 2004.
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 2004 and 2012?
Answer:
Least Common Multiple of 2004 and 2012 = 1008012
Step 1: Find the prime factorization of 2004
2004 = 2 x 2 x 3 x 167
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 = 1008012 = 2 x 2 x 3 x 167 x 503
Step 4: Therefore, the least common multiple of 2004 and 2012 is 1008012.