Least Common Multiple (LCM) of 128 and 75
The least common multiple (LCM) of 128 and 75 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 128 and 75?
First, calculate the GCD of 128 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 75 = 1 remainder 53 |
| 2 | 75 ÷ 53 = 1 remainder 22 |
| 3 | 53 ÷ 22 = 2 remainder 9 |
| 4 | 22 ÷ 9 = 2 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 38 | 7030 |
| 145 and 37 | 5365 |
| 89 and 120 | 10680 |
| 155 and 85 | 2635 |
| 197 and 127 | 25019 |