Least Common Multiple (LCM) of 11 and 199
The least common multiple (LCM) of 11 and 199 is 2189.
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 11 and 199?
First, calculate the GCD of 11 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 11 ÷ 199 = 0 remainder 11 |
| 2 | 199 ÷ 11 = 18 remainder 1 |
| 3 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 56 | 112 |
| 193 and 144 | 27792 |
| 65 and 165 | 2145 |
| 133 and 107 | 14231 |
| 113 and 182 | 20566 |