Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 998 and 1004 the smallest integer that is 500996 that is divisible by both numbers.
Least Common Multiple (LCM) of 998 and 1004 is 500996.
LCM(998,1004) = 500996
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 998 and 1004. First we will calculate the prime factors of 998 and 1004.
Prime Factorization of 998
2 | 998 |
499 | 499 |
1 |
Prime factors of 998 are 2,499. Prime factorization of 998 in exponential form is:
998 = 21×4991
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
Now multiplying the highest exponent prime factors to calculate the LCM of 998 and 1004.
LCM(998,1004) = 22×2511×4991
LCM(998,1004) = 500996
Factors of 998
List of positive integer factors of 998 that divides 998 without a remainder.
1, 2, 499, 998
Factors of 1004
List of positive integer factors of 1004 that divides 1004 without a remainder.
1, 2, 4, 251, 502, 1004
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 998 and 1004, than apply into the LCM equation.
GCF(998,1004) = 2
LCM(998,1004) = ( 998 × 1004) / 2
LCM(998,1004) = 1001992 / 2
LCM(998,1004) = 500996
(i) The LCM of 1004 and 998 is associative
LCM of 998 and 1004 = LCM of 1004 and 998
1. What is the LCM of 998 and 1004?
Answer: LCM of 998 and 1004 is 500996.
2. What are the Factors of 998?
Answer: Factors of 998 are 1, 2, 499, 998. There are 4 integers that are factors of 998. The greatest factor of 998 is 998.
3. 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.
4. How to Find the LCM of 998 and 1004?
Answer:
Least Common Multiple of 998 and 1004 = 500996
Step 1: Find the prime factorization of 998
998 = 2 x 499
Step 2: Find the prime factorization of 1004
1004 = 2 x 2 x 251
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 500996 = 2 x 2 x 251 x 499
Step 4: Therefore, the least common multiple of 998 and 1004 is 500996.