Least Common Multiple (LCM) of 82 and 197
The least common multiple (LCM) of 82 and 197 is 16154.
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 197?
First, calculate the GCD of 82 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 197 = 0 remainder 82 |
| 2 | 197 ÷ 82 = 2 remainder 33 |
| 3 | 82 ÷ 33 = 2 remainder 16 |
| 4 | 33 ÷ 16 = 2 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 199 | 35820 |
| 13 and 63 | 819 |
| 75 and 107 | 8025 |
| 191 and 164 | 31324 |
| 37 and 14 | 518 |