Least Common Multiple (LCM) of 50 and 128
The least common multiple (LCM) of 50 and 128 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 50 and 128?
First, calculate the GCD of 50 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 128 = 0 remainder 50 |
| 2 | 128 ÷ 50 = 2 remainder 28 |
| 3 | 50 ÷ 28 = 1 remainder 22 |
| 4 | 28 ÷ 22 = 1 remainder 6 |
| 5 | 22 ÷ 6 = 3 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 119 | 3213 |
| 33 and 80 | 2640 |
| 86 and 49 | 4214 |
| 54 and 178 | 4806 |
| 126 and 149 | 18774 |