Least Common Multiple of 2010 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 2010 and 2014 the smallest integer that is 2024070 that is divisible by both numbers.
Least Common Multiple (LCM) of 2010 and 2014 is 2024070.
LCM(2010,2014) = 2024070
LCM of 2010 and 2014
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2010 and 2014 by Prime method
- Least Common Multiple of 2010 and 2014 with GCF Formula
LCM of 2010 and 2014 is 2024070
Least common multiple can be found by multiplying the highest exponent prime factors of 2010 and 2014. First we will calculate the prime factors of 2010 and 2014.
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
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 2010 and 2014.
LCM(2010,2014) = 21×31×51×191×531×671
LCM(2010,2014) = 2024070
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
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 2010 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 2010 and 2014, than apply into the LCM equation.
GCF(2010,2014) = 2
LCM(2010,2014) = ( 2010 × 2014) / 2
LCM(2010,2014) = 4048140 / 2
LCM(2010,2014) = 2024070
Properties of LCM 2010 and 2014
(i) The LCM of 2014 and 2010 is associative
LCM of 2010 and 2014 = LCM of 2014 and 2010
Related Least Common Multiples of 2010
Related Least Common Multiples of 2014
Frequently Asked Questions on LCM of 2010 and 2014
1. What is the LCM of 2010 and 2014?
Answer: LCM of 2010 and 2014 is 2024070.
2. 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.
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 2010 and 2014?
Answer:
Least Common Multiple of 2010 and 2014 = 2024070
Step 1: Find the prime factorization of 2010
2010 = 2 x 3 x 5 x 67
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 = 2024070 = 2 x 3 x 5 x 19 x 53 x 67
Step 4: Therefore, the least common multiple of 2010 and 2014 is 2024070.