Least Common Multiple (LCM) of 82 and 199
The least common multiple (LCM) of 82 and 199 is 16318.
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 199?
First, calculate the GCD of 82 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 199 = 0 remainder 82 |
| 2 | 199 ÷ 82 = 2 remainder 35 |
| 3 | 82 ÷ 35 = 2 remainder 12 |
| 4 | 35 ÷ 12 = 2 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 43 | 1075 |
| 98 and 133 | 1862 |
| 71 and 178 | 12638 |
| 79 and 68 | 5372 |
| 149 and 122 | 18178 |