Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3078 and 3082 the smallest integer that is 4743198 that is divisible by both numbers.
Least Common Multiple (LCM) of 3078 and 3082 is 4743198.
LCM(3078,3082) = 4743198
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 3078 and 3082. First we will calculate the prime factors of 3078 and 3082.
Prime Factorization of 3078
2 | 3078 |
3 | 1539 |
3 | 513 |
3 | 171 |
3 | 57 |
19 | 19 |
1 |
Prime factors of 3078 are 2, 3,19. Prime factorization of 3078 in exponential form is:
3078 = 21×34×191
Prime Factorization of 3082
2 | 3082 |
23 | 1541 |
67 | 67 |
1 |
Prime factors of 3082 are 2, 23,67. Prime factorization of 3082 in exponential form is:
3082 = 21×231×671
Now multiplying the highest exponent prime factors to calculate the LCM of 3078 and 3082.
LCM(3078,3082) = 21×34×191×231×671
LCM(3078,3082) = 4743198
Factors of 3078
List of positive integer factors of 3078 that divides 3078 without a remainder.
1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 81, 114, 162, 171, 342, 513, 1026, 1539, 3078
Factors of 3082
List of positive integer factors of 3082 that divides 3082 without a remainder.
1, 2, 23, 46, 67, 134, 1541, 3082
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3078 and 3082, than apply into the LCM equation.
GCF(3078,3082) = 2
LCM(3078,3082) = ( 3078 × 3082) / 2
LCM(3078,3082) = 9486396 / 2
LCM(3078,3082) = 4743198
(i) The LCM of 3082 and 3078 is associative
LCM of 3078 and 3082 = LCM of 3082 and 3078
1. What is the LCM of 3078 and 3082?
Answer: LCM of 3078 and 3082 is 4743198.
2. What are the Factors of 3078?
Answer: Factors of 3078 are 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 81, 114, 162, 171, 342, 513, 1026, 1539, 3078. There are 20 integers that are factors of 3078. The greatest factor of 3078 is 3078.
3. What are the Factors of 3082?
Answer: Factors of 3082 are 1, 2, 23, 46, 67, 134, 1541, 3082. There are 8 integers that are factors of 3082. The greatest factor of 3082 is 3082.
4. How to Find the LCM of 3078 and 3082?
Answer:
Least Common Multiple of 3078 and 3082 = 4743198
Step 1: Find the prime factorization of 3078
3078 = 2 x 3 x 3 x 3 x 3 x 19
Step 2: Find the prime factorization of 3082
3082 = 2 x 23 x 67
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4743198 = 2 x 3 x 3 x 3 x 3 x 19 x 23 x 67
Step 4: Therefore, the least common multiple of 3078 and 3082 is 4743198.