Least Common Multiple (LCM) of 82 and 193
The least common multiple (LCM) of 82 and 193 is 15826.
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 193?
First, calculate the GCD of 82 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 193 = 0 remainder 82 |
| 2 | 193 ÷ 82 = 2 remainder 29 |
| 3 | 82 ÷ 29 = 2 remainder 24 |
| 4 | 29 ÷ 24 = 1 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 21 | 2730 |
| 154 and 47 | 7238 |
| 198 and 199 | 39402 |
| 185 and 80 | 2960 |
| 29 and 30 | 870 |