Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7998 and 8006 the smallest integer that is 32015994 that is divisible by both numbers.
Least Common Multiple (LCM) of 7998 and 8006 is 32015994.
LCM(7998,8006) = 32015994
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 7998 and 8006. First we will calculate the prime factors of 7998 and 8006.
Prime Factorization of 7998
2 | 7998 |
3 | 3999 |
31 | 1333 |
43 | 43 |
1 |
Prime factors of 7998 are 2, 3, 31,43. Prime factorization of 7998 in exponential form is:
7998 = 21×31×311×431
Prime Factorization of 8006
2 | 8006 |
4003 | 4003 |
1 |
Prime factors of 8006 are 2,4003. Prime factorization of 8006 in exponential form is:
8006 = 21×40031
Now multiplying the highest exponent prime factors to calculate the LCM of 7998 and 8006.
LCM(7998,8006) = 21×31×311×431×40031
LCM(7998,8006) = 32015994
Factors of 7998
List of positive integer factors of 7998 that divides 7998 without a remainder.
1, 2, 3, 6, 31, 43, 62, 86, 93, 129, 186, 258, 1333, 2666, 3999, 7998
Factors of 8006
List of positive integer factors of 8006 that divides 8006 without a remainder.
1, 2, 4003, 8006
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7998 and 8006, than apply into the LCM equation.
GCF(7998,8006) = 2
LCM(7998,8006) = ( 7998 × 8006) / 2
LCM(7998,8006) = 64031988 / 2
LCM(7998,8006) = 32015994
(i) The LCM of 8006 and 7998 is associative
LCM of 7998 and 8006 = LCM of 8006 and 7998
1. What is the LCM of 7998 and 8006?
Answer: LCM of 7998 and 8006 is 32015994.
2. What are the Factors of 7998?
Answer: Factors of 7998 are 1, 2, 3, 6, 31, 43, 62, 86, 93, 129, 186, 258, 1333, 2666, 3999, 7998. There are 16 integers that are factors of 7998. The greatest factor of 7998 is 7998.
3. What are the Factors of 8006?
Answer: Factors of 8006 are 1, 2, 4003, 8006. There are 4 integers that are factors of 8006. The greatest factor of 8006 is 8006.
4. How to Find the LCM of 7998 and 8006?
Answer:
Least Common Multiple of 7998 and 8006 = 32015994
Step 1: Find the prime factorization of 7998
7998 = 2 x 3 x 31 x 43
Step 2: Find the prime factorization of 8006
8006 = 2 x 4003
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 32015994 = 2 x 3 x 31 x 43 x 4003
Step 4: Therefore, the least common multiple of 7998 and 8006 is 32015994.