Least Common Multiple (LCM) of 114 and 129
The least common multiple (LCM) of 114 and 129 is 4902.
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 114 and 129?
First, calculate the GCD of 114 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 129 = 0 remainder 114 |
| 2 | 129 ÷ 114 = 1 remainder 15 |
| 3 | 114 ÷ 15 = 7 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 134 | 26666 |
| 69 and 115 | 345 |
| 171 and 163 | 27873 |
| 83 and 193 | 16019 |
| 74 and 23 | 1702 |