Least Common Multiple (LCM) of 193 and 198
The least common multiple (LCM) of 193 and 198 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 193 and 198?
First, calculate the GCD of 193 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 198 = 0 remainder 193 |
| 2 | 198 ÷ 193 = 1 remainder 5 |
| 3 | 193 ÷ 5 = 38 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 41 | 1312 |
| 111 and 161 | 17871 |
| 106 and 55 | 5830 |
| 194 and 107 | 20758 |
| 73 and 164 | 11972 |