Least Common Multiple (LCM) of 198 and 193
The least common multiple (LCM) of 198 and 193 is 38214.
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 193?
First, calculate the GCD of 198 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 193 = 1 remainder 5 |
| 2 | 193 ÷ 5 = 38 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 10 | 230 |
| 200 and 108 | 5400 |
| 106 and 56 | 2968 |
| 194 and 78 | 7566 |
| 50 and 96 | 2400 |