Least Common Multiple of 2010 and 2013
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 2013 the smallest integer that is 1348710 that is divisible by both numbers.
Least Common Multiple (LCM) of 2010 and 2013 is 1348710.
LCM(2010,2013) = 1348710
LCM of 2010 and 2013
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 2010 and 2013 by Prime method
- Least Common Multiple of 2010 and 2013 with GCF Formula
LCM of 2010 and 2013 is 1348710
Least common multiple can be found by multiplying the highest exponent prime factors of 2010 and 2013. First we will calculate the prime factors of 2010 and 2013.
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 2013
| 3 | 2013 |
| 11 | 671 |
| 61 | 61 |
| 1 |
Prime factors of 2013 are 3, 11,61. Prime factorization of 2013 in exponential form is:
2013 = 31×111×611
Now multiplying the highest exponent prime factors to calculate the LCM of 2010 and 2013.
LCM(2010,2013) = 21×31×51×111×611×671
LCM(2010,2013) = 1348710
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 2013
List of positive integer factors of 2013 that divides 2013 without a remainder.
1, 3, 11, 33, 61, 183, 671, 2013
Least Common Multiple of 2010 and 2013 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 2013, than apply into the LCM equation.
GCF(2010,2013) = 3
LCM(2010,2013) = ( 2010 × 2013) / 3
LCM(2010,2013) = 4046130 / 3
LCM(2010,2013) = 1348710
Properties of LCM 2010 and 2013
(i) The LCM of 2013 and 2010 is associative
LCM of 2010 and 2013 = LCM of 2013 and 2010
Related Least Common Multiples of 2010
Related Least Common Multiples of 2013
Frequently Asked Questions on LCM of 2010 and 2013
1. What is the LCM of 2010 and 2013?
Answer: LCM of 2010 and 2013 is 1348710.
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 2013?
Answer: Factors of 2013 are 1, 3, 11, 33, 61, 183, 671, 2013. There are 8 integers that are factors of 2013. The greatest factor of 2013 is 2013.
4. How to Find the LCM of 2010 and 2013?
Answer:
Least Common Multiple of 2010 and 2013 = 1348710
Step 1: Find the prime factorization of 2010
2010 = 2 x 3 x 5 x 67
Step 2: Find the prime factorization of 2013
2013 = 3 x 11 x 61
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1348710 = 2 x 3 x 5 x 11 x 61 x 67
Step 4: Therefore, the least common multiple of 2010 and 2013 is 1348710.