Least Common Multiple (LCM) of 128 and 50
The least common multiple (LCM) of 128 and 50 is 3200.
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 128 and 50?
First, calculate the GCD of 128 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 50 = 2 remainder 28 |
| 2 | 50 ÷ 28 = 1 remainder 22 |
| 3 | 28 ÷ 22 = 1 remainder 6 |
| 4 | 22 ÷ 6 = 3 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 115 | 16790 |
| 157 and 126 | 19782 |
| 103 and 187 | 19261 |
| 72 and 84 | 504 |
| 143 and 27 | 3861 |