Least Common Multiple (LCM) of 17 and 199
The least common multiple (LCM) of 17 and 199 is 3383.
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 199?
First, calculate the GCD of 17 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 199 = 0 remainder 17 |
| 2 | 199 ÷ 17 = 11 remainder 12 |
| 3 | 17 ÷ 12 = 1 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 54 | 378 |
| 109 and 135 | 14715 |
| 144 and 82 | 5904 |
| 190 and 96 | 9120 |
| 164 and 116 | 4756 |