Least Common Multiple (LCM) of 75 and 128
The least common multiple (LCM) of 75 and 128 is 9600.
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 75 and 128?
First, calculate the GCD of 75 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 128 = 0 remainder 75 |
| 2 | 128 ÷ 75 = 1 remainder 53 |
| 3 | 75 ÷ 53 = 1 remainder 22 |
| 4 | 53 ÷ 22 = 2 remainder 9 |
| 5 | 22 ÷ 9 = 2 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 77 | 385 |
| 192 and 95 | 18240 |
| 108 and 41 | 4428 |
| 177 and 165 | 9735 |
| 170 and 180 | 3060 |