Least Common Multiple (LCM) of 65 and 129
The least common multiple (LCM) of 65 and 129 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 65 and 129?
First, calculate the GCD of 65 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 129 = 0 remainder 65 |
| 2 | 129 ÷ 65 = 1 remainder 64 |
| 3 | 65 ÷ 64 = 1 remainder 1 |
| 4 | 64 ÷ 1 = 64 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 189 | 31374 |
| 184 and 181 | 33304 |
| 83 and 122 | 10126 |
| 190 and 27 | 5130 |
| 167 and 132 | 22044 |