Least Common Multiple (LCM) of 50 and 83
The least common multiple (LCM) of 50 and 83 is 4150.
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 83?
First, calculate the GCD of 50 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 83 = 0 remainder 50 |
| 2 | 83 ÷ 50 = 1 remainder 33 |
| 3 | 50 ÷ 33 = 1 remainder 17 |
| 4 | 33 ÷ 17 = 1 remainder 16 |
| 5 | 17 ÷ 16 = 1 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 96 | 96 |
| 50 and 63 | 3150 |
| 166 and 102 | 8466 |
| 178 and 139 | 24742 |
| 64 and 73 | 4672 |