Least Common Multiple of 2009 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 2009 and 2010 the smallest integer that is 4038090 that is divisible by both numbers.
Least Common Multiple (LCM) of 2009 and 2010 is 4038090.
LCM(2009,2010) = 4038090
LCM of 2009 and 2010
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2009 and 2010 by Prime method
- Least Common Multiple of 2009 and 2010 with GCF Formula
LCM of 2009 and 2010 is 4038090
Least common multiple can be found by multiplying the highest exponent prime factors of 2009 and 2010. First we will calculate the prime factors of 2009 and 2010.
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
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 2009 and 2010.
LCM(2009,2010) = 21×31×51×72×411×671
LCM(2009,2010) = 4038090
Factors of 2009
List of positive integer factors of 2009 that divides 2009 without a remainder.
1, 7, 41, 49, 287, 2009
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 2009 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 2009 and 2010, than apply into the LCM equation.
GCF(2009,2010) = 1
LCM(2009,2010) = ( 2009 × 2010) / 1
LCM(2009,2010) = 4038090 / 1
LCM(2009,2010) = 4038090
Properties of LCM 2009 and 2010
(i) The LCM of 2010 and 2009 is associative
LCM of 2009 and 2010 = LCM of 2010 and 2009
Related Least Common Multiples of 2009
Related Least Common Multiples of 2010
Frequently Asked Questions on LCM of 2009 and 2010
1. What is the LCM of 2009 and 2010?
Answer: LCM of 2009 and 2010 is 4038090.
2. 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.
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 2009 and 2010?
Answer:
Least Common Multiple of 2009 and 2010 = 4038090
Step 1: Find the prime factorization of 2009
2009 = 7 x 7 x 41
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 = 4038090 = 2 x 3 x 5 x 7 x 7 x 41 x 67
Step 4: Therefore, the least common multiple of 2009 and 2010 is 4038090.