Least Common Multiple (LCM) of 115 and 129
The least common multiple (LCM) of 115 and 129 is 14835.
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 115 and 129?
First, calculate the GCD of 115 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 129 = 0 remainder 115 |
| 2 | 129 ÷ 115 = 1 remainder 14 |
| 3 | 115 ÷ 14 = 8 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 26 and 107 | 2782 |
| 156 and 146 | 11388 |
| 190 and 192 | 18240 |
| 64 and 45 | 2880 |
| 191 and 186 | 35526 |