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 8032 the smallest integer that is 8056096 that is divisible by both numbers.
Least Common Multiple (LCM) of 8024 and 8032 is 8056096.
LCM(8024,8032) = 8056096
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 8032. First we will calculate the prime factors of 8024 and 8032.
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 8032
2 | 8032 |
2 | 4016 |
2 | 2008 |
2 | 1004 |
2 | 502 |
251 | 251 |
1 |
Prime factors of 8032 are 2,251. Prime factorization of 8032 in exponential form is:
8032 = 25×2511
Now multiplying the highest exponent prime factors to calculate the LCM of 8024 and 8032.
LCM(8024,8032) = 25×171×591×2511
LCM(8024,8032) = 8056096
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 8032
List of positive integer factors of 8032 that divides 8032 without a remainder.
1, 2, 4, 8, 16, 32, 251, 502, 1004, 2008, 4016, 8032
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8024 and 8032, than apply into the LCM equation.
GCF(8024,8032) = 8
LCM(8024,8032) = ( 8024 × 8032) / 8
LCM(8024,8032) = 64448768 / 8
LCM(8024,8032) = 8056096
(i) The LCM of 8032 and 8024 is associative
LCM of 8024 and 8032 = LCM of 8032 and 8024
1. What is the LCM of 8024 and 8032?
Answer: LCM of 8024 and 8032 is 8056096.
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 8032?
Answer: Factors of 8032 are 1, 2, 4, 8, 16, 32, 251, 502, 1004, 2008, 4016, 8032. There are 12 integers that are factors of 8032. The greatest factor of 8032 is 8032.
4. How to Find the LCM of 8024 and 8032?
Answer:
Least Common Multiple of 8024 and 8032 = 8056096
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 8032
8032 = 2 x 2 x 2 x 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 = 8056096 = 2 x 2 x 2 x 2 x 2 x 17 x 59 x 251
Step 4: Therefore, the least common multiple of 8024 and 8032 is 8056096.