Least Common Multiple of 2007 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 2007 and 2014 the smallest integer that is 4042098 that is divisible by both numbers.
Least Common Multiple (LCM) of 2007 and 2014 is 4042098.
LCM(2007,2014) = 4042098
LCM of 2007 and 2014
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2007 and 2014 by Prime method
- Least Common Multiple of 2007 and 2014 with GCF Formula
LCM of 2007 and 2014 is 4042098
Least common multiple can be found by multiplying the highest exponent prime factors of 2007 and 2014. First we will calculate the prime factors of 2007 and 2014.
Prime Factorization of 2007
| 3 | 2007 |
| 3 | 669 |
| 223 | 223 |
| 1 |
Prime factors of 2007 are 3,223. Prime factorization of 2007 in exponential form is:
2007 = 32×2231
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 2007 and 2014.
LCM(2007,2014) = 21×32×191×531×2231
LCM(2007,2014) = 4042098
Factors of 2007
List of positive integer factors of 2007 that divides 2007 without a remainder.
1, 3, 9, 223, 669, 2007
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 2007 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 2007 and 2014, than apply into the LCM equation.
GCF(2007,2014) = 1
LCM(2007,2014) = ( 2007 × 2014) / 1
LCM(2007,2014) = 4042098 / 1
LCM(2007,2014) = 4042098
Properties of LCM 2007 and 2014
(i) The LCM of 2014 and 2007 is associative
LCM of 2007 and 2014 = LCM of 2014 and 2007
Related Least Common Multiples of 2007
Related Least Common Multiples of 2014
Frequently Asked Questions on LCM of 2007 and 2014
1. What is the LCM of 2007 and 2014?
Answer: LCM of 2007 and 2014 is 4042098.
2. What are the Factors of 2007?
Answer: Factors of 2007 are 1, 3, 9, 223, 669, 2007. There are 6 integers that are factors of 2007. The greatest factor of 2007 is 2007.
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 2007 and 2014?
Answer:
Least Common Multiple of 2007 and 2014 = 4042098
Step 1: Find the prime factorization of 2007
2007 = 3 x 3 x 223
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 = 4042098 = 2 x 3 x 3 x 19 x 53 x 223
Step 4: Therefore, the least common multiple of 2007 and 2014 is 4042098.
