Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1004 and 1006 the smallest integer that is 505012 that is divisible by both numbers.
Least Common Multiple (LCM) of 1004 and 1006 is 505012.
LCM(1004,1006) = 505012
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 1004 and 1006. First we will calculate the prime factors of 1004 and 1006.
Prime Factorization of 1004
2 | 1004 |
2 | 502 |
251 | 251 |
1 |
Prime factors of 1004 are 2,251. Prime factorization of 1004 in exponential form is:
1004 = 22×2511
Prime Factorization of 1006
2 | 1006 |
503 | 503 |
1 |
Prime factors of 1006 are 2,503. Prime factorization of 1006 in exponential form is:
1006 = 21×5031
Now multiplying the highest exponent prime factors to calculate the LCM of 1004 and 1006.
LCM(1004,1006) = 22×2511×5031
LCM(1004,1006) = 505012
Factors of 1004
List of positive integer factors of 1004 that divides 1004 without a remainder.
1, 2, 4, 251, 502, 1004
Factors of 1006
List of positive integer factors of 1006 that divides 1006 without a remainder.
1, 2, 503, 1006
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1004 and 1006, than apply into the LCM equation.
GCF(1004,1006) = 2
LCM(1004,1006) = ( 1004 × 1006) / 2
LCM(1004,1006) = 1010024 / 2
LCM(1004,1006) = 505012
(i) The LCM of 1006 and 1004 is associative
LCM of 1004 and 1006 = LCM of 1006 and 1004
1. What is the LCM of 1004 and 1006?
Answer: LCM of 1004 and 1006 is 505012.
2. What are the Factors of 1004?
Answer: Factors of 1004 are 1, 2, 4, 251, 502, 1004. There are 6 integers that are factors of 1004. The greatest factor of 1004 is 1004.
3. What are the Factors of 1006?
Answer: Factors of 1006 are 1, 2, 503, 1006. There are 4 integers that are factors of 1006. The greatest factor of 1006 is 1006.
4. How to Find the LCM of 1004 and 1006?
Answer:
Least Common Multiple of 1004 and 1006 = 505012
Step 1: Find the prime factorization of 1004
1004 = 2 x 2 x 251
Step 2: Find the prime factorization of 1006
1006 = 2 x 503
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 505012 = 2 x 2 x 251 x 503
Step 4: Therefore, the least common multiple of 1004 and 1006 is 505012.