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 8028 the smallest integer that is 10733436 that is divisible by both numbers.
Least Common Multiple (LCM) of 8022 and 8028 is 10733436.
LCM(8022,8028) = 10733436
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 8028. First we will calculate the prime factors of 8022 and 8028.
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 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 8022 and 8028.
LCM(8022,8028) = 22×32×71×1911×2231
LCM(8022,8028) = 10733436
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 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 8022 and 8028, than apply into the LCM equation.
GCF(8022,8028) = 6
LCM(8022,8028) = ( 8022 × 8028) / 6
LCM(8022,8028) = 64400616 / 6
LCM(8022,8028) = 10733436
(i) The LCM of 8028 and 8022 is associative
LCM of 8022 and 8028 = LCM of 8028 and 8022
1. What is the LCM of 8022 and 8028?
Answer: LCM of 8022 and 8028 is 10733436.
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 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 8022 and 8028?
Answer:
Least Common Multiple of 8022 and 8028 = 10733436
Step 1: Find the prime factorization of 8022
8022 = 2 x 3 x 7 x 191
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 = 10733436 = 2 x 2 x 3 x 3 x 7 x 191 x 223
Step 4: Therefore, the least common multiple of 8022 and 8028 is 10733436.