Least Common Multiple of 2009 and 2015
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 2015 the smallest integer that is 4048135 that is divisible by both numbers.
Least Common Multiple (LCM) of 2009 and 2015 is 4048135.
LCM(2009,2015) = 4048135
LCM of 2009 and 2015
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2009 and 2015 by Prime method
- Least Common Multiple of 2009 and 2015 with GCF Formula
LCM of 2009 and 2015 is 4048135
Least common multiple can be found by multiplying the highest exponent prime factors of 2009 and 2015. First we will calculate the prime factors of 2009 and 2015.
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 2015
| 5 | 2015 |
| 13 | 403 |
| 31 | 31 |
| 1 |
Prime factors of 2015 are 5, 13,31. Prime factorization of 2015 in exponential form is:
2015 = 51×131×311
Now multiplying the highest exponent prime factors to calculate the LCM of 2009 and 2015.
LCM(2009,2015) = 51×72×131×311×411
LCM(2009,2015) = 4048135
Factors of 2009
List of positive integer factors of 2009 that divides 2009 without a remainder.
1, 7, 41, 49, 287, 2009
Factors of 2015
List of positive integer factors of 2015 that divides 2015 without a remainder.
1, 5, 13, 31, 65, 155, 403, 2015
Least Common Multiple of 2009 and 2015 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 2015, than apply into the LCM equation.
GCF(2009,2015) = 1
LCM(2009,2015) = ( 2009 × 2015) / 1
LCM(2009,2015) = 4048135 / 1
LCM(2009,2015) = 4048135
Properties of LCM 2009 and 2015
(i) The LCM of 2015 and 2009 is associative
LCM of 2009 and 2015 = LCM of 2015 and 2009
Related Least Common Multiples of 2009
Related Least Common Multiples of 2015
Frequently Asked Questions on LCM of 2009 and 2015
1. What is the LCM of 2009 and 2015?
Answer: LCM of 2009 and 2015 is 4048135.
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 2015?
Answer: Factors of 2015 are 1, 5, 13, 31, 65, 155, 403, 2015. There are 8 integers that are factors of 2015. The greatest factor of 2015 is 2015.
4. How to Find the LCM of 2009 and 2015?
Answer:
Least Common Multiple of 2009 and 2015 = 4048135
Step 1: Find the prime factorization of 2009
2009 = 7 x 7 x 41
Step 2: Find the prime factorization of 2015
2015 = 5 x 13 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4048135 = 5 x 7 x 7 x 13 x 31 x 41
Step 4: Therefore, the least common multiple of 2009 and 2015 is 4048135.
