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 1008 the smallest integer that is 253008 that is divisible by both numbers.
Least Common Multiple (LCM) of 1004 and 1008 is 253008.
LCM(1004,1008) = 253008
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 1008. First we will calculate the prime factors of 1004 and 1008.
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 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 1004 and 1008.
LCM(1004,1008) = 24×32×71×2511
LCM(1004,1008) = 253008
Factors of 1004
List of positive integer factors of 1004 that divides 1004 without a remainder.
1, 2, 4, 251, 502, 1004
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 1004 and 1008, than apply into the LCM equation.
GCF(1004,1008) = 4
LCM(1004,1008) = ( 1004 × 1008) / 4
LCM(1004,1008) = 1012032 / 4
LCM(1004,1008) = 253008
(i) The LCM of 1008 and 1004 is associative
LCM of 1004 and 1008 = LCM of 1008 and 1004
1. What is the LCM of 1004 and 1008?
Answer: LCM of 1004 and 1008 is 253008.
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 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 1004 and 1008?
Answer:
Least Common Multiple of 1004 and 1008 = 253008
Step 1: Find the prime factorization of 1004
1004 = 2 x 2 x 251
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 = 253008 = 2 x 2 x 2 x 2 x 3 x 3 x 7 x 251
Step 4: Therefore, the least common multiple of 1004 and 1008 is 253008.