Least Common Multiple (LCM) of 82 and 198
The least common multiple (LCM) of 82 and 198 is 8118.
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 82 and 198?
First, calculate the GCD of 82 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 198 = 0 remainder 82 |
| 2 | 198 ÷ 82 = 2 remainder 34 |
| 3 | 82 ÷ 34 = 2 remainder 14 |
| 4 | 34 ÷ 14 = 2 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 10 | 260 |
| 35 and 196 | 980 |
| 189 and 30 | 1890 |
| 11 and 34 | 374 |
| 105 and 119 | 1785 |