Least Common Multiple (LCM) of 17 and 198
The least common multiple (LCM) of 17 and 198 is 3366.
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 17 and 198?
First, calculate the GCD of 17 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 198 = 0 remainder 17 |
| 2 | 198 ÷ 17 = 11 remainder 11 |
| 3 | 17 ÷ 11 = 1 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 90 | 180 |
| 142 and 177 | 25134 |
| 119 and 137 | 16303 |
| 193 and 106 | 20458 |
| 46 and 49 | 2254 |