Least Common Multiple (LCM) of 83 and 129
The least common multiple (LCM) of 83 and 129 is 10707.
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 83 and 129?
First, calculate the GCD of 83 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 129 = 0 remainder 83 |
| 2 | 129 ÷ 83 = 1 remainder 46 |
| 3 | 83 ÷ 46 = 1 remainder 37 |
| 4 | 46 ÷ 37 = 1 remainder 9 |
| 5 | 37 ÷ 9 = 4 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 10 | 430 |
| 126 and 117 | 1638 |
| 65 and 32 | 2080 |
| 185 and 182 | 33670 |
| 82 and 141 | 11562 |