Least Common Multiple (LCM) of 82 and 99
The least common multiple (LCM) of 82 and 99 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 82 and 99?
First, calculate the GCD of 82 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 99 = 0 remainder 82 |
| 2 | 99 ÷ 82 = 1 remainder 17 |
| 3 | 82 ÷ 17 = 4 remainder 14 |
| 4 | 17 ÷ 14 = 1 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 197 | 7880 |
| 172 and 123 | 21156 |
| 93 and 35 | 3255 |
| 47 and 59 | 2773 |
| 180 and 177 | 10620 |