Least Common Multiple (LCM) of 128 and 195
The least common multiple (LCM) of 128 and 195 is 24960.
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 195?
First, calculate the GCD of 128 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 195 = 0 remainder 128 |
| 2 | 195 ÷ 128 = 1 remainder 67 |
| 3 | 128 ÷ 67 = 1 remainder 61 |
| 4 | 67 ÷ 61 = 1 remainder 6 |
| 5 | 61 ÷ 6 = 10 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 94 and 175 | 16450 |
| 54 and 45 | 270 |
| 107 and 165 | 17655 |
| 170 and 165 | 5610 |
| 89 and 88 | 7832 |