Least Common Multiple (LCM) of 82 and 108
The least common multiple (LCM) of 82 and 108 is 4428.
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 108?
First, calculate the GCD of 82 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 108 = 0 remainder 82 |
| 2 | 108 ÷ 82 = 1 remainder 26 |
| 3 | 82 ÷ 26 = 3 remainder 4 |
| 4 | 26 ÷ 4 = 6 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 44 | 3916 |
| 166 and 101 | 16766 |
| 122 and 180 | 10980 |
| 63 and 54 | 378 |
| 143 and 122 | 17446 |