Least Common Multiple (LCM) of 199 and 82
The least common multiple (LCM) of 199 and 82 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 199 and 82?
First, calculate the GCD of 199 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 82 = 2 remainder 35 |
| 2 | 82 ÷ 35 = 2 remainder 12 |
| 3 | 35 ÷ 12 = 2 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 43 | 3096 |
| 54 and 71 | 3834 |
| 172 and 67 | 11524 |
| 21 and 28 | 84 |
| 44 and 111 | 4884 |