Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7997 and 8004 the smallest integer that is 64007988 that is divisible by both numbers.
Least Common Multiple (LCM) of 7997 and 8004 is 64007988.
LCM(7997,8004) = 64007988
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 7997 and 8004. First we will calculate the prime factors of 7997 and 8004.
Prime Factorization of 7997
11 | 7997 |
727 | 727 |
1 |
Prime factors of 7997 are 11,727. Prime factorization of 7997 in exponential form is:
7997 = 111×7271
Prime Factorization of 8004
2 | 8004 |
2 | 4002 |
3 | 2001 |
23 | 667 |
29 | 29 |
1 |
Prime factors of 8004 are 2, 3, 23,29. Prime factorization of 8004 in exponential form is:
8004 = 22×31×231×291
Now multiplying the highest exponent prime factors to calculate the LCM of 7997 and 8004.
LCM(7997,8004) = 22×31×111×231×291×7271
LCM(7997,8004) = 64007988
Factors of 7997
List of positive integer factors of 7997 that divides 7997 without a remainder.
1, 11, 727, 7997
Factors of 8004
List of positive integer factors of 8004 that divides 8004 without a remainder.
1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 8004
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7997 and 8004, than apply into the LCM equation.
GCF(7997,8004) = 1
LCM(7997,8004) = ( 7997 × 8004) / 1
LCM(7997,8004) = 64007988 / 1
LCM(7997,8004) = 64007988
(i) The LCM of 8004 and 7997 is associative
LCM of 7997 and 8004 = LCM of 8004 and 7997
1. What is the LCM of 7997 and 8004?
Answer: LCM of 7997 and 8004 is 64007988.
2. What are the Factors of 7997?
Answer: Factors of 7997 are 1, 11, 727, 7997. There are 4 integers that are factors of 7997. The greatest factor of 7997 is 7997.
3. What are the Factors of 8004?
Answer: Factors of 8004 are 1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 8004. There are 24 integers that are factors of 8004. The greatest factor of 8004 is 8004.
4. How to Find the LCM of 7997 and 8004?
Answer:
Least Common Multiple of 7997 and 8004 = 64007988
Step 1: Find the prime factorization of 7997
7997 = 11 x 727
Step 2: Find the prime factorization of 8004
8004 = 2 x 2 x 3 x 23 x 29
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 64007988 = 2 x 2 x 3 x 11 x 23 x 29 x 727
Step 4: Therefore, the least common multiple of 7997 and 8004 is 64007988.