Least Common Multiple (LCM) of 129 and 71
The least common multiple (LCM) of 129 and 71 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 129 and 71?
First, calculate the GCD of 129 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 71 = 1 remainder 58 |
| 2 | 71 ÷ 58 = 1 remainder 13 |
| 3 | 58 ÷ 13 = 4 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 18 | 198 |
| 53 and 122 | 6466 |
| 170 and 54 | 4590 |
| 99 and 100 | 9900 |
| 124 and 171 | 21204 |