Least Common Multiple of 1003 and 1005
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1003 and 1005 the smallest integer that is 1008015 that is divisible by both numbers.
Least Common Multiple (LCM) of 1003 and 1005 is 1008015.
LCM(1003,1005) = 1008015
LCM of 1003 and 1005
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 1003 and 1005 by Prime method
- Least Common Multiple of 1003 and 1005 with GCF Formula
LCM of 1003 and 1005 is 1008015
Least common multiple can be found by multiplying the highest exponent prime factors of 1003 and 1005. First we will calculate the prime factors of 1003 and 1005.
Prime Factorization of 1003
| 17 | 1003 |
| 59 | 59 |
| 1 |
Prime factors of 1003 are 17,59. Prime factorization of 1003 in exponential form is:
1003 = 171×591
Prime Factorization of 1005
| 3 | 1005 |
| 5 | 335 |
| 67 | 67 |
| 1 |
Prime factors of 1005 are 3, 5,67. Prime factorization of 1005 in exponential form is:
1005 = 31×51×671
Now multiplying the highest exponent prime factors to calculate the LCM of 1003 and 1005.
LCM(1003,1005) = 31×51×171×591×671
LCM(1003,1005) = 1008015
Factors of 1003
List of positive integer factors of 1003 that divides 1003 without a remainder.
1, 17, 59, 1003
Factors of 1005
List of positive integer factors of 1005 that divides 1005 without a remainder.
1, 3, 5, 15, 67, 201, 335, 1005
Least Common Multiple of 1003 and 1005 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1003 and 1005, than apply into the LCM equation.
GCF(1003,1005) = 1
LCM(1003,1005) = ( 1003 × 1005) / 1
LCM(1003,1005) = 1008015 / 1
LCM(1003,1005) = 1008015
Properties of LCM 1003 and 1005
(i) The LCM of 1005 and 1003 is associative
LCM of 1003 and 1005 = LCM of 1005 and 1003
Related Least Common Multiples of 1003
Related Least Common Multiples of 1005
Frequently Asked Questions on LCM of 1003 and 1005
1. What is the LCM of 1003 and 1005?
Answer: LCM of 1003 and 1005 is 1008015.
2. What are the Factors of 1003?
Answer: Factors of 1003 are 1, 17, 59, 1003. There are 4 integers that are factors of 1003. The greatest factor of 1003 is 1003.
3. What are the Factors of 1005?
Answer: Factors of 1005 are 1, 3, 5, 15, 67, 201, 335, 1005. There are 8 integers that are factors of 1005. The greatest factor of 1005 is 1005.
4. How to Find the LCM of 1003 and 1005?
Answer:
Least Common Multiple of 1003 and 1005 = 1008015
Step 1: Find the prime factorization of 1003
1003 = 17 x 59
Step 2: Find the prime factorization of 1005
1005 = 3 x 5 x 67
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1008015 = 3 x 5 x 17 x 59 x 67
Step 4: Therefore, the least common multiple of 1003 and 1005 is 1008015.
