Least Common Multiple (LCM) of 50 and 82
The least common multiple (LCM) of 50 and 82 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 50 and 82?
First, calculate the GCD of 50 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 82 = 0 remainder 50 |
| 2 | 82 ÷ 50 = 1 remainder 32 |
| 3 | 50 ÷ 32 = 1 remainder 18 |
| 4 | 32 ÷ 18 = 1 remainder 14 |
| 5 | 18 ÷ 14 = 1 remainder 4 |
| 6 | 14 ÷ 4 = 3 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 88 | 11880 |
| 22 and 157 | 3454 |
| 105 and 137 | 14385 |
| 49 and 80 | 3920 |
| 78 and 62 | 2418 |