Least Common Multiple (LCM) of 128 and 189
The least common multiple (LCM) of 128 and 189 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 128 and 189?
First, calculate the GCD of 128 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 189 = 0 remainder 128 |
| 2 | 189 ÷ 128 = 1 remainder 61 |
| 3 | 128 ÷ 61 = 2 remainder 6 |
| 4 | 61 ÷ 6 = 10 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 182 | 4914 |
| 35 and 57 | 1995 |
| 195 and 101 | 19695 |
| 136 and 85 | 680 |
| 128 and 59 | 7552 |