Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8024 and 8031 the smallest integer that is 64440744 that is divisible by both numbers.
Least Common Multiple (LCM) of 8024 and 8031 is 64440744.
LCM(8024,8031) = 64440744
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 8024 and 8031. First we will calculate the prime factors of 8024 and 8031.
Prime Factorization of 8024
2 | 8024 |
2 | 4012 |
2 | 2006 |
17 | 1003 |
59 | 59 |
1 |
Prime factors of 8024 are 2, 17,59. Prime factorization of 8024 in exponential form is:
8024 = 23×171×591
Prime Factorization of 8031
3 | 8031 |
2677 | 2677 |
1 |
Prime factors of 8031 are 3,2677. Prime factorization of 8031 in exponential form is:
8031 = 31×26771
Now multiplying the highest exponent prime factors to calculate the LCM of 8024 and 8031.
LCM(8024,8031) = 23×31×171×591×26771
LCM(8024,8031) = 64440744
Factors of 8024
List of positive integer factors of 8024 that divides 8024 without a remainder.
1, 2, 4, 8, 17, 34, 59, 68, 118, 136, 236, 472, 1003, 2006, 4012, 8024
Factors of 8031
List of positive integer factors of 8031 that divides 8031 without a remainder.
1, 3, 2677, 8031
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8024 and 8031, than apply into the LCM equation.
GCF(8024,8031) = 1
LCM(8024,8031) = ( 8024 × 8031) / 1
LCM(8024,8031) = 64440744 / 1
LCM(8024,8031) = 64440744
(i) The LCM of 8031 and 8024 is associative
LCM of 8024 and 8031 = LCM of 8031 and 8024
1. What is the LCM of 8024 and 8031?
Answer: LCM of 8024 and 8031 is 64440744.
2. What are the Factors of 8024?
Answer: Factors of 8024 are 1, 2, 4, 8, 17, 34, 59, 68, 118, 136, 236, 472, 1003, 2006, 4012, 8024. There are 16 integers that are factors of 8024. The greatest factor of 8024 is 8024.
3. What are the Factors of 8031?
Answer: Factors of 8031 are 1, 3, 2677, 8031. There are 4 integers that are factors of 8031. The greatest factor of 8031 is 8031.
4. How to Find the LCM of 8024 and 8031?
Answer:
Least Common Multiple of 8024 and 8031 = 64440744
Step 1: Find the prime factorization of 8024
8024 = 2 x 2 x 2 x 17 x 59
Step 2: Find the prime factorization of 8031
8031 = 3 x 2677
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 64440744 = 2 x 2 x 2 x 3 x 17 x 59 x 2677
Step 4: Therefore, the least common multiple of 8024 and 8031 is 64440744.