Least Common Multiple (LCM) of 82 and 50
The least common multiple (LCM) of 82 and 50 is 2050.
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 50?
First, calculate the GCD of 82 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 50 = 1 remainder 32 |
| 2 | 50 ÷ 32 = 1 remainder 18 |
| 3 | 32 ÷ 18 = 1 remainder 14 |
| 4 | 18 ÷ 14 = 1 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 20 | 380 |
| 141 and 83 | 11703 |
| 120 and 66 | 1320 |
| 172 and 45 | 7740 |
| 130 and 20 | 260 |