Least Common Multiple (LCM) of 82 and 105
The least common multiple (LCM) of 82 and 105 is 8610.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 82 and 105?
First, calculate the GCD of 82 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 105 = 0 remainder 82 |
| 2 | 105 ÷ 82 = 1 remainder 23 |
| 3 | 82 ÷ 23 = 3 remainder 13 |
| 4 | 23 ÷ 13 = 1 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 104 | 936 |
| 57 and 11 | 627 |
| 94 and 164 | 7708 |
| 186 and 94 | 8742 |
| 187 and 164 | 30668 |