Least Common Multiple (LCM) of 50 and 117
The least common multiple (LCM) of 50 and 117 is 5850.
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 117?
First, calculate the GCD of 50 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 117 = 0 remainder 50 |
| 2 | 117 ÷ 50 = 2 remainder 17 |
| 3 | 50 ÷ 17 = 2 remainder 16 |
| 4 | 17 ÷ 16 = 1 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 168 | 17976 |
| 46 and 11 | 506 |
| 49 and 44 | 2156 |
| 157 and 115 | 18055 |
| 163 and 96 | 15648 |