Least Common Multiple (LCM) of 89 and 199
The least common multiple (LCM) of 89 and 199 is 17711.
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 89 and 199?
First, calculate the GCD of 89 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 199 = 0 remainder 89 |
| 2 | 199 ÷ 89 = 2 remainder 21 |
| 3 | 89 ÷ 21 = 4 remainder 5 |
| 4 | 21 ÷ 5 = 4 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 10 | 1890 |
| 169 and 192 | 32448 |
| 200 and 130 | 2600 |
| 196 and 161 | 4508 |
| 57 and 177 | 3363 |