Least Common Multiple of 1000 and 1001
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1000 and 1001 the smallest integer that is 1001000 that is divisible by both numbers.
Least Common Multiple (LCM) of 1000 and 1001 is 1001000.
LCM(1000,1001) = 1001000
LCM of 1000 and 1001
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 1000 and 1001 by Prime method
- Least Common Multiple of 1000 and 1001 with GCF Formula
LCM of 1000 and 1001 is 1001000
Least common multiple can be found by multiplying the highest exponent prime factors of 1000 and 1001. First we will calculate the prime factors of 1000 and 1001.
Prime Factorization of 1000
| 2 | 1000 |
| 2 | 500 |
| 2 | 250 |
| 5 | 125 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 1000 are 2,5. Prime factorization of 1000 in exponential form is:
1000 = 23×53
Prime Factorization of 1001
| 7 | 1001 |
| 11 | 143 |
| 13 | 13 |
| 1 |
Prime factors of 1001 are 7, 11,13. Prime factorization of 1001 in exponential form is:
1001 = 71×111×131
Now multiplying the highest exponent prime factors to calculate the LCM of 1000 and 1001.
LCM(1000,1001) = 23×53×71×111×131
LCM(1000,1001) = 1001000
Factors of 1000
List of positive integer factors of 1000 that divides 1000 without a remainder.
1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
Factors of 1001
List of positive integer factors of 1001 that divides 1001 without a remainder.
1, 7, 11, 13, 77, 91, 143, 1001
Least Common Multiple of 1000 and 1001 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1000 and 1001, than apply into the LCM equation.
GCF(1000,1001) = 1
LCM(1000,1001) = ( 1000 × 1001) / 1
LCM(1000,1001) = 1001000 / 1
LCM(1000,1001) = 1001000
Properties of LCM 1000 and 1001
(i) The LCM of 1001 and 1000 is associative
LCM of 1000 and 1001 = LCM of 1001 and 1000
Related Least Common Multiples of 1000
Related Least Common Multiples of 1001
Frequently Asked Questions on LCM of 1000 and 1001
1. What is the LCM of 1000 and 1001?
Answer: LCM of 1000 and 1001 is 1001000.
2. What are the Factors of 1000?
Answer: Factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000. There are 16 integers that are factors of 1000. The greatest factor of 1000 is 1000.
3. What are the Factors of 1001?
Answer: Factors of 1001 are 1, 7, 11, 13, 77, 91, 143, 1001. There are 8 integers that are factors of 1001. The greatest factor of 1001 is 1001.
4. How to Find the LCM of 1000 and 1001?
Answer:
Least Common Multiple of 1000 and 1001 = 1001000
Step 1: Find the prime factorization of 1000
1000 = 2 x 2 x 2 x 5 x 5 x 5
Step 2: Find the prime factorization of 1001
1001 = 7 x 11 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 = 1001000 = 2 x 2 x 2 x 5 x 5 x 5 x 7 x 11 x 13
Step 4: Therefore, the least common multiple of 1000 and 1001 is 1001000.
