Least Common Multiple (LCM) of 198 and 128
The least common multiple (LCM) of 198 and 128 is 12672.
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 198 and 128?
First, calculate the GCD of 198 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 128 = 1 remainder 70 |
| 2 | 128 ÷ 70 = 1 remainder 58 |
| 3 | 70 ÷ 58 = 1 remainder 12 |
| 4 | 58 ÷ 12 = 4 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 129 | 1032 |
| 157 and 139 | 21823 |
| 172 and 123 | 21156 |
| 10 and 27 | 270 |
| 161 and 32 | 5152 |