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 8028 the smallest integer that is 16104168 that is divisible by both numbers.
Least Common Multiple (LCM) of 8024 and 8028 is 16104168.
LCM(8024,8028) = 16104168
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 8028. First we will calculate the prime factors of 8024 and 8028.
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 8028
2 | 8028 |
2 | 4014 |
3 | 2007 |
3 | 669 |
223 | 223 |
1 |
Prime factors of 8028 are 2, 3,223. Prime factorization of 8028 in exponential form is:
8028 = 22×32×2231
Now multiplying the highest exponent prime factors to calculate the LCM of 8024 and 8028.
LCM(8024,8028) = 23×32×171×591×2231
LCM(8024,8028) = 16104168
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 8028
List of positive integer factors of 8028 that divides 8028 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 36, 223, 446, 669, 892, 1338, 2007, 2676, 4014, 8028
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8024 and 8028, than apply into the LCM equation.
GCF(8024,8028) = 4
LCM(8024,8028) = ( 8024 × 8028) / 4
LCM(8024,8028) = 64416672 / 4
LCM(8024,8028) = 16104168
(i) The LCM of 8028 and 8024 is associative
LCM of 8024 and 8028 = LCM of 8028 and 8024
1. What is the LCM of 8024 and 8028?
Answer: LCM of 8024 and 8028 is 16104168.
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 8028?
Answer: Factors of 8028 are 1, 2, 3, 4, 6, 9, 12, 18, 36, 223, 446, 669, 892, 1338, 2007, 2676, 4014, 8028. There are 18 integers that are factors of 8028. The greatest factor of 8028 is 8028.
4. How to Find the LCM of 8024 and 8028?
Answer:
Least Common Multiple of 8024 and 8028 = 16104168
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 8028
8028 = 2 x 2 x 3 x 3 x 223
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 16104168 = 2 x 2 x 2 x 3 x 3 x 17 x 59 x 223
Step 4: Therefore, the least common multiple of 8024 and 8028 is 16104168.