Least Common Multiple (LCM) of 82 and 125
The least common multiple (LCM) of 82 and 125 is 10250.
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 125?
First, calculate the GCD of 82 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 125 = 0 remainder 82 |
| 2 | 125 ÷ 82 = 1 remainder 43 |
| 3 | 82 ÷ 43 = 1 remainder 39 |
| 4 | 43 ÷ 39 = 1 remainder 4 |
| 5 | 39 ÷ 4 = 9 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 80 | 80 |
| 200 and 117 | 23400 |
| 83 and 155 | 12865 |
| 34 and 172 | 2924 |
| 192 and 125 | 24000 |