Least Common Multiple of 2004 and 2010
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 2010 the smallest integer that is 671340 that is divisible by both numbers.
Least Common Multiple (LCM) of 2004 and 2010 is 671340.
LCM(2004,2010) = 671340
LCM of 2004 and 2010
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2004 and 2010 by Prime method
- Least Common Multiple of 2004 and 2010 with GCF Formula
LCM of 2004 and 2010 is 671340
Least common multiple can be found by multiplying the highest exponent prime factors of 2004 and 2010. First we will calculate the prime factors of 2004 and 2010.
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 2010
| 2 | 2010 |
| 3 | 1005 |
| 5 | 335 |
| 67 | 67 |
| 1 |
Prime factors of 2010 are 2, 3, 5,67. Prime factorization of 2010 in exponential form is:
2010 = 21×31×51×671
Now multiplying the highest exponent prime factors to calculate the LCM of 2004 and 2010.
LCM(2004,2010) = 22×31×51×671×1671
LCM(2004,2010) = 671340
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 2010
List of positive integer factors of 2010 that divides 2010 without a remainder.
1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010
Least Common Multiple of 2004 and 2010 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 2010, than apply into the LCM equation.
GCF(2004,2010) = 6
LCM(2004,2010) = ( 2004 × 2010) / 6
LCM(2004,2010) = 4028040 / 6
LCM(2004,2010) = 671340
Properties of LCM 2004 and 2010
(i) The LCM of 2010 and 2004 is associative
LCM of 2004 and 2010 = LCM of 2010 and 2004
Related Least Common Multiples of 2004
Related Least Common Multiples of 2010
Frequently Asked Questions on LCM of 2004 and 2010
1. What is the LCM of 2004 and 2010?
Answer: LCM of 2004 and 2010 is 671340.
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 2010?
Answer: Factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010. There are 16 integers that are factors of 2010. The greatest factor of 2010 is 2010.
4. How to Find the LCM of 2004 and 2010?
Answer:
Least Common Multiple of 2004 and 2010 = 671340
Step 1: Find the prime factorization of 2004
2004 = 2 x 2 x 3 x 167
Step 2: Find the prime factorization of 2010
2010 = 2 x 3 x 5 x 67
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 671340 = 2 x 2 x 3 x 5 x 67 x 167
Step 4: Therefore, the least common multiple of 2004 and 2010 is 671340.