Least Common Multiple (LCM) of 50 and 86
The least common multiple (LCM) of 50 and 86 is 2150.
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 86?
First, calculate the GCD of 50 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 86 = 0 remainder 50 |
| 2 | 86 ÷ 50 = 1 remainder 36 |
| 3 | 50 ÷ 36 = 1 remainder 14 |
| 4 | 36 ÷ 14 = 2 remainder 8 |
| 5 | 14 ÷ 8 = 1 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 51 | 5712 |
| 139 and 171 | 23769 |
| 24 and 190 | 2280 |
| 100 and 135 | 2700 |
| 189 and 13 | 2457 |