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 |
|---|---|
| 148 and 197 | 29156 |
| 113 and 67 | 7571 |
| 152 and 97 | 14744 |
| 158 and 144 | 11376 |
| 115 and 198 | 22770 |