Least Common Multiple (LCM) of 198 and 82
The least common multiple (LCM) of 198 and 82 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 198 and 82?
First, calculate the GCD of 198 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 82 = 2 remainder 34 |
| 2 | 82 ÷ 34 = 2 remainder 14 |
| 3 | 34 ÷ 14 = 2 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 47 | 6815 |
| 195 and 122 | 23790 |
| 107 and 31 | 3317 |
| 129 and 134 | 17286 |
| 48 and 46 | 1104 |