Least Common Multiple (LCM) of 189 and 128
The least common multiple (LCM) of 189 and 128 is 24192.
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 189 and 128?
First, calculate the GCD of 189 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 128 = 1 remainder 61 |
| 2 | 128 ÷ 61 = 2 remainder 6 |
| 3 | 61 ÷ 6 = 10 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 32 | 1120 |
| 144 and 177 | 8496 |
| 76 and 193 | 14668 |
| 176 and 189 | 33264 |
| 149 and 118 | 17582 |