Least Common Multiple (LCM) of 129 and 65
The least common multiple (LCM) of 129 and 65 is 8385.
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 65?
First, calculate the GCD of 129 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 65 = 1 remainder 64 |
| 2 | 65 ÷ 64 = 1 remainder 1 |
| 3 | 64 ÷ 1 = 64 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 129 | 18318 |
| 72 and 34 | 1224 |
| 151 and 22 | 3322 |
| 121 and 155 | 18755 |
| 151 and 71 | 10721 |