Least Common Multiple (LCM) of 199 and 17
The least common multiple (LCM) of 199 and 17 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 199 and 17?
First, calculate the GCD of 199 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 17 = 11 remainder 12 |
| 2 | 17 ÷ 12 = 1 remainder 5 |
| 3 | 12 ÷ 5 = 2 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 119 | 119 |
| 17 and 160 | 2720 |
| 137 and 191 | 26167 |
| 137 and 115 | 15755 |
| 110 and 199 | 21890 |