Least Common Multiple of 2006 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 2006 and 2014 the smallest integer that is 2020042 that is divisible by both numbers.
Least Common Multiple (LCM) of 2006 and 2014 is 2020042.
LCM(2006,2014) = 2020042
LCM of 2006 and 2014
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2006 and 2014 by Prime method
- Least Common Multiple of 2006 and 2014 with GCF Formula
LCM of 2006 and 2014 is 2020042
Least common multiple can be found by multiplying the highest exponent prime factors of 2006 and 2014. First we will calculate the prime factors of 2006 and 2014.
Prime Factorization of 2006
| 2 | 2006 |
| 17 | 1003 |
| 59 | 59 |
| 1 |
Prime factors of 2006 are 2, 17,59. Prime factorization of 2006 in exponential form is:
2006 = 21×171×591
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 2006 and 2014.
LCM(2006,2014) = 21×171×191×531×591
LCM(2006,2014) = 2020042
Factors of 2006
List of positive integer factors of 2006 that divides 2006 without a remainder.
1, 2, 17, 34, 59, 118, 1003, 2006
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 2006 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 2006 and 2014, than apply into the LCM equation.
GCF(2006,2014) = 2
LCM(2006,2014) = ( 2006 × 2014) / 2
LCM(2006,2014) = 4040084 / 2
LCM(2006,2014) = 2020042
Properties of LCM 2006 and 2014
(i) The LCM of 2014 and 2006 is associative
LCM of 2006 and 2014 = LCM of 2014 and 2006
Related Least Common Multiples of 2006
Related Least Common Multiples of 2014
Frequently Asked Questions on LCM of 2006 and 2014
1. What is the LCM of 2006 and 2014?
Answer: LCM of 2006 and 2014 is 2020042.
2. What are the Factors of 2006?
Answer: Factors of 2006 are 1, 2, 17, 34, 59, 118, 1003, 2006. There are 8 integers that are factors of 2006. The greatest factor of 2006 is 2006.
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 2006 and 2014?
Answer:
Least Common Multiple of 2006 and 2014 = 2020042
Step 1: Find the prime factorization of 2006
2006 = 2 x 17 x 59
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 = 2020042 = 2 x 17 x 19 x 53 x 59
Step 4: Therefore, the least common multiple of 2006 and 2014 is 2020042.
