Least Common Multiple (LCM) of 129 and 82
The least common multiple (LCM) of 129 and 82 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 129 and 82?
First, calculate the GCD of 129 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 82 = 1 remainder 47 |
| 2 | 82 ÷ 47 = 1 remainder 35 |
| 3 | 47 ÷ 35 = 1 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 |
|---|---|
| 98 and 101 | 9898 |
| 97 and 103 | 9991 |
| 128 and 103 | 13184 |
| 192 and 85 | 16320 |
| 138 and 108 | 2484 |