Least Common Multiple (LCM) of 82 and 57
The least common multiple (LCM) of 82 and 57 is 4674.
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 57?
First, calculate the GCD of 82 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 57 = 1 remainder 25 |
| 2 | 57 ÷ 25 = 2 remainder 7 |
| 3 | 25 ÷ 7 = 3 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 92 | 3404 |
| 197 and 17 | 3349 |
| 126 and 91 | 1638 |
| 130 and 101 | 13130 |
| 41 and 82 | 82 |