Least Common Multiple of 2004 and 2009
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 2009 the smallest integer that is 4026036 that is divisible by both numbers.
Least Common Multiple (LCM) of 2004 and 2009 is 4026036.
LCM(2004,2009) = 4026036
LCM of 2004 and 2009
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2004 and 2009 by Prime method
- Least Common Multiple of 2004 and 2009 with GCF Formula
LCM of 2004 and 2009 is 4026036
Least common multiple can be found by multiplying the highest exponent prime factors of 2004 and 2009. First we will calculate the prime factors of 2004 and 2009.
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 2009
| 7 | 2009 |
| 7 | 287 |
| 41 | 41 |
| 1 |
Prime factors of 2009 are 7,41. Prime factorization of 2009 in exponential form is:
2009 = 72×411
Now multiplying the highest exponent prime factors to calculate the LCM of 2004 and 2009.
LCM(2004,2009) = 22×31×72×411×1671
LCM(2004,2009) = 4026036
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 2009
List of positive integer factors of 2009 that divides 2009 without a remainder.
1, 7, 41, 49, 287, 2009
Least Common Multiple of 2004 and 2009 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 2009, than apply into the LCM equation.
GCF(2004,2009) = 1
LCM(2004,2009) = ( 2004 × 2009) / 1
LCM(2004,2009) = 4026036 / 1
LCM(2004,2009) = 4026036
Properties of LCM 2004 and 2009
(i) The LCM of 2009 and 2004 is associative
LCM of 2004 and 2009 = LCM of 2009 and 2004
Related Least Common Multiples of 2004
Related Least Common Multiples of 2009
Frequently Asked Questions on LCM of 2004 and 2009
1. What is the LCM of 2004 and 2009?
Answer: LCM of 2004 and 2009 is 4026036.
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 2009?
Answer: Factors of 2009 are 1, 7, 41, 49, 287, 2009. There are 6 integers that are factors of 2009. The greatest factor of 2009 is 2009.
4. How to Find the LCM of 2004 and 2009?
Answer:
Least Common Multiple of 2004 and 2009 = 4026036
Step 1: Find the prime factorization of 2004
2004 = 2 x 2 x 3 x 167
Step 2: Find the prime factorization of 2009
2009 = 7 x 7 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4026036 = 2 x 2 x 3 x 7 x 7 x 41 x 167
Step 4: Therefore, the least common multiple of 2004 and 2009 is 4026036.
