Least Common Multiple (LCM) of 128 and 198
The least common multiple (LCM) of 128 and 198 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 128 and 198?
First, calculate the GCD of 128 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 198 = 0 remainder 128 |
| 2 | 198 ÷ 128 = 1 remainder 70 |
| 3 | 128 ÷ 70 = 1 remainder 58 |
| 4 | 70 ÷ 58 = 1 remainder 12 |
| 5 | 58 ÷ 12 = 4 remainder 10 |
| 6 | 12 ÷ 10 = 1 remainder 2 |
| 7 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 139 | 8062 |
| 34 and 19 | 646 |
| 137 and 14 | 1918 |
| 52 and 19 | 988 |
| 134 and 190 | 12730 |