Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1006 and 1008 the smallest integer that is 507024 that is divisible by both numbers.
Least Common Multiple (LCM) of 1006 and 1008 is 507024.
LCM(1006,1008) = 507024
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 1006 and 1008. First we will calculate the prime factors of 1006 and 1008.
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
Prime Factorization of 1008
2 | 1008 |
2 | 504 |
2 | 252 |
2 | 126 |
3 | 63 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 1008 are 2, 3,7. Prime factorization of 1008 in exponential form is:
1008 = 24×32×71
Now multiplying the highest exponent prime factors to calculate the LCM of 1006 and 1008.
LCM(1006,1008) = 24×32×71×5031
LCM(1006,1008) = 507024
Factors of 1006
List of positive integer factors of 1006 that divides 1006 without a remainder.
1, 2, 503, 1006
Factors of 1008
List of positive integer factors of 1008 that divides 1008 without a remainder.
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1006 and 1008, than apply into the LCM equation.
GCF(1006,1008) = 2
LCM(1006,1008) = ( 1006 × 1008) / 2
LCM(1006,1008) = 1014048 / 2
LCM(1006,1008) = 507024
(i) The LCM of 1008 and 1006 is associative
LCM of 1006 and 1008 = LCM of 1008 and 1006
1. What is the LCM of 1006 and 1008?
Answer: LCM of 1006 and 1008 is 507024.
2. 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.
3. What are the Factors of 1008?
Answer: Factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008. There are 30 integers that are factors of 1008. The greatest factor of 1008 is 1008.
4. How to Find the LCM of 1006 and 1008?
Answer:
Least Common Multiple of 1006 and 1008 = 507024
Step 1: Find the prime factorization of 1006
1006 = 2 x 503
Step 2: Find the prime factorization of 1008
1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 507024 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 503
Step 4: Therefore, the least common multiple of 1006 and 1008 is 507024.