Least Common Multiple of 1007 and 1014
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1007 and 1014 the smallest integer that is 1021098 that is divisible by both numbers.
Least Common Multiple (LCM) of 1007 and 1014 is 1021098.
LCM(1007,1014) = 1021098
LCM of 1007 and 1014
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 1007 and 1014 by Prime method
- Least Common Multiple of 1007 and 1014 with GCF Formula
LCM of 1007 and 1014 is 1021098
Least common multiple can be found by multiplying the highest exponent prime factors of 1007 and 1014. First we will calculate the prime factors of 1007 and 1014.
Prime Factorization of 1007
| 19 | 1007 |
| 53 | 53 |
| 1 |
Prime factors of 1007 are 19,53. Prime factorization of 1007 in exponential form is:
1007 = 191×531
Prime Factorization of 1014
| 2 | 1014 |
| 3 | 507 |
| 13 | 169 |
| 13 | 13 |
| 1 |
Prime factors of 1014 are 2, 3,13. Prime factorization of 1014 in exponential form is:
1014 = 21×31×132
Now multiplying the highest exponent prime factors to calculate the LCM of 1007 and 1014.
LCM(1007,1014) = 21×31×132×191×531
LCM(1007,1014) = 1021098
Factors of 1007
List of positive integer factors of 1007 that divides 1007 without a remainder.
1, 19, 53, 1007
Factors of 1014
List of positive integer factors of 1014 that divides 1014 without a remainder.
1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014
Least Common Multiple of 1007 and 1014 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1007 and 1014, than apply into the LCM equation.
GCF(1007,1014) = 1
LCM(1007,1014) = ( 1007 × 1014) / 1
LCM(1007,1014) = 1021098 / 1
LCM(1007,1014) = 1021098
Properties of LCM 1007 and 1014
(i) The LCM of 1014 and 1007 is associative
LCM of 1007 and 1014 = LCM of 1014 and 1007
Related Least Common Multiples of 1007
Related Least Common Multiples of 1014
Frequently Asked Questions on LCM of 1007 and 1014
1. What is the LCM of 1007 and 1014?
Answer: LCM of 1007 and 1014 is 1021098.
2. What are the Factors of 1007?
Answer: Factors of 1007 are 1, 19, 53, 1007. There are 4 integers that are factors of 1007. The greatest factor of 1007 is 1007.
3. What are the Factors of 1014?
Answer: Factors of 1014 are 1, 2, 3, 6, 13, 26, 39, 78, 169, 338, 507, 1014. There are 12 integers that are factors of 1014. The greatest factor of 1014 is 1014.
4. How to Find the LCM of 1007 and 1014?
Answer:
Least Common Multiple of 1007 and 1014 = 1021098
Step 1: Find the prime factorization of 1007
1007 = 19 x 53
Step 2: Find the prime factorization of 1014
1014 = 2 x 3 x 13 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1021098 = 2 x 3 x 13 x 13 x 19 x 53
Step 4: Therefore, the least common multiple of 1007 and 1014 is 1021098.