Least Common Multiple (LCM) of 82 and 129
The least common multiple (LCM) of 82 and 129 is 10578.
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 129?
First, calculate the GCD of 82 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 129 = 0 remainder 82 |
| 2 | 129 ÷ 82 = 1 remainder 47 |
| 3 | 82 ÷ 47 = 1 remainder 35 |
| 4 | 47 ÷ 35 = 1 remainder 12 |
| 5 | 35 ÷ 12 = 2 remainder 11 |
| 6 | 12 ÷ 11 = 1 remainder 1 |
| 7 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 135 | 6345 |
| 168 and 172 | 7224 |
| 196 and 188 | 9212 |
| 13 and 75 | 975 |
| 199 and 141 | 28059 |