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 8030 the smallest integer that is 32216360 that is divisible by both numbers.
Least Common Multiple (LCM) of 8024 and 8030 is 32216360.
LCM(8024,8030) = 32216360
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 8030. First we will calculate the prime factors of 8024 and 8030.
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 8030
2 | 8030 |
5 | 4015 |
11 | 803 |
73 | 73 |
1 |
Prime factors of 8030 are 2, 5, 11,73. Prime factorization of 8030 in exponential form is:
8030 = 21×51×111×731
Now multiplying the highest exponent prime factors to calculate the LCM of 8024 and 8030.
LCM(8024,8030) = 23×51×111×171×591×731
LCM(8024,8030) = 32216360
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 8030
List of positive integer factors of 8030 that divides 8030 without a remainder.
1, 2, 5, 10, 11, 22, 55, 73, 110, 146, 365, 730, 803, 1606, 4015, 8030
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8024 and 8030, than apply into the LCM equation.
GCF(8024,8030) = 2
LCM(8024,8030) = ( 8024 × 8030) / 2
LCM(8024,8030) = 64432720 / 2
LCM(8024,8030) = 32216360
(i) The LCM of 8030 and 8024 is associative
LCM of 8024 and 8030 = LCM of 8030 and 8024
1. What is the LCM of 8024 and 8030?
Answer: LCM of 8024 and 8030 is 32216360.
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 8030?
Answer: Factors of 8030 are 1, 2, 5, 10, 11, 22, 55, 73, 110, 146, 365, 730, 803, 1606, 4015, 8030. There are 16 integers that are factors of 8030. The greatest factor of 8030 is 8030.
4. How to Find the LCM of 8024 and 8030?
Answer:
Least Common Multiple of 8024 and 8030 = 32216360
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 8030
8030 = 2 x 5 x 11 x 73
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 32216360 = 2 x 2 x 2 x 5 x 11 x 17 x 59 x 73
Step 4: Therefore, the least common multiple of 8024 and 8030 is 32216360.