Least Common Multiple (LCM) of 50 and 193
The least common multiple (LCM) of 50 and 193 is 9650.
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 193?
First, calculate the GCD of 50 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 193 = 0 remainder 50 |
| 2 | 193 ÷ 50 = 3 remainder 43 |
| 3 | 50 ÷ 43 = 1 remainder 7 |
| 4 | 43 ÷ 7 = 6 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 13 | 2587 |
| 94 and 67 | 6298 |
| 132 and 36 | 396 |
| 114 and 86 | 4902 |
| 174 and 108 | 3132 |