Least Common Multiple (LCM) of 128 and 199
The least common multiple (LCM) of 128 and 199 is 25472.
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 199?
First, calculate the GCD of 128 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 199 = 0 remainder 128 |
| 2 | 199 ÷ 128 = 1 remainder 71 |
| 3 | 128 ÷ 71 = 1 remainder 57 |
| 4 | 71 ÷ 57 = 1 remainder 14 |
| 5 | 57 ÷ 14 = 4 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 117 | 351 |
| 107 and 19 | 2033 |
| 165 and 23 | 3795 |
| 170 and 47 | 7990 |
| 84 and 117 | 3276 |