Least Common Multiple of 2009 and 2014
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 2014 the smallest integer that is 4046126 that is divisible by both numbers.
Least Common Multiple (LCM) of 2009 and 2014 is 4046126.
LCM(2009,2014) = 4046126
LCM of 2009 and 2014
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2009 and 2014 by Prime method
- Least Common Multiple of 2009 and 2014 with GCF Formula
LCM of 2009 and 2014 is 4046126
Least common multiple can be found by multiplying the highest exponent prime factors of 2009 and 2014. First we will calculate the prime factors of 2009 and 2014.
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 2014
| 2 | 2014 |
| 19 | 1007 |
| 53 | 53 |
| 1 |
Prime factors of 2014 are 2, 19,53. Prime factorization of 2014 in exponential form is:
2014 = 21×191×531
Now multiplying the highest exponent prime factors to calculate the LCM of 2009 and 2014.
LCM(2009,2014) = 21×72×191×411×531
LCM(2009,2014) = 4046126
Factors of 2009
List of positive integer factors of 2009 that divides 2009 without a remainder.
1, 7, 41, 49, 287, 2009
Factors of 2014
List of positive integer factors of 2014 that divides 2014 without a remainder.
1, 2, 19, 38, 53, 106, 1007, 2014
Least Common Multiple of 2009 and 2014 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 2014, than apply into the LCM equation.
GCF(2009,2014) = 1
LCM(2009,2014) = ( 2009 × 2014) / 1
LCM(2009,2014) = 4046126 / 1
LCM(2009,2014) = 4046126
Properties of LCM 2009 and 2014
(i) The LCM of 2014 and 2009 is associative
LCM of 2009 and 2014 = LCM of 2014 and 2009
Related Least Common Multiples of 2009
Related Least Common Multiples of 2014
Frequently Asked Questions on LCM of 2009 and 2014
1. What is the LCM of 2009 and 2014?
Answer: LCM of 2009 and 2014 is 4046126.
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 2014?
Answer: Factors of 2014 are 1, 2, 19, 38, 53, 106, 1007, 2014. There are 8 integers that are factors of 2014. The greatest factor of 2014 is 2014.
4. How to Find the LCM of 2009 and 2014?
Answer:
Least Common Multiple of 2009 and 2014 = 4046126
Step 1: Find the prime factorization of 2009
2009 = 7 x 7 x 41
Step 2: Find the prime factorization of 2014
2014 = 2 x 19 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4046126 = 2 x 7 x 7 x 19 x 41 x 53
Step 4: Therefore, the least common multiple of 2009 and 2014 is 4046126.