Least Common Multiple (LCM) of 50 and 111
The least common multiple (LCM) of 50 and 111 is 5550.
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 111?
First, calculate the GCD of 50 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 111 = 0 remainder 50 |
| 2 | 111 ÷ 50 = 2 remainder 11 |
| 3 | 50 ÷ 11 = 4 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 155 | 29915 |
| 161 and 25 | 4025 |
| 193 and 44 | 8492 |
| 96 and 51 | 1632 |
| 99 and 196 | 19404 |