Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8022 and 8030 the smallest integer that is 32208330 that is divisible by both numbers.
Least Common Multiple (LCM) of 8022 and 8030 is 32208330.
LCM(8022,8030) = 32208330
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 8022 and 8030. First we will calculate the prime factors of 8022 and 8030.
Prime Factorization of 8022
2 | 8022 |
3 | 4011 |
7 | 1337 |
191 | 191 |
1 |
Prime factors of 8022 are 2, 3, 7,191. Prime factorization of 8022 in exponential form is:
8022 = 21×31×71×1911
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 8022 and 8030.
LCM(8022,8030) = 21×31×51×71×111×731×1911
LCM(8022,8030) = 32208330
Factors of 8022
List of positive integer factors of 8022 that divides 8022 without a remainder.
1, 2, 3, 6, 7, 14, 21, 42, 191, 382, 573, 1146, 1337, 2674, 4011, 8022
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 8022 and 8030, than apply into the LCM equation.
GCF(8022,8030) = 2
LCM(8022,8030) = ( 8022 × 8030) / 2
LCM(8022,8030) = 64416660 / 2
LCM(8022,8030) = 32208330
(i) The LCM of 8030 and 8022 is associative
LCM of 8022 and 8030 = LCM of 8030 and 8022
1. What is the LCM of 8022 and 8030?
Answer: LCM of 8022 and 8030 is 32208330.
2. What are the Factors of 8022?
Answer: Factors of 8022 are 1, 2, 3, 6, 7, 14, 21, 42, 191, 382, 573, 1146, 1337, 2674, 4011, 8022. There are 16 integers that are factors of 8022. The greatest factor of 8022 is 8022.
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 8022 and 8030?
Answer:
Least Common Multiple of 8022 and 8030 = 32208330
Step 1: Find the prime factorization of 8022
8022 = 2 x 3 x 7 x 191
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 = 32208330 = 2 x 3 x 5 x 7 x 11 x 73 x 191
Step 4: Therefore, the least common multiple of 8022 and 8030 is 32208330.