Least Common Multiple (LCM) of 71 and 129
The least common multiple (LCM) of 71 and 129 is 9159.
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 71 and 129?
First, calculate the GCD of 71 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 129 = 0 remainder 71 |
| 2 | 129 ÷ 71 = 1 remainder 58 |
| 3 | 71 ÷ 58 = 1 remainder 13 |
| 4 | 58 ÷ 13 = 4 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 192 | 4800 |
| 200 and 58 | 5800 |
| 96 and 48 | 96 |
| 82 and 89 | 7298 |
| 113 and 10 | 1130 |