Least Common Multiple (LCM) of 129 and 114
The least common multiple (LCM) of 129 and 114 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 129 and 114?
First, calculate the GCD of 129 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 114 = 1 remainder 15 |
| 2 | 114 ÷ 15 = 7 remainder 9 |
| 3 | 15 ÷ 9 = 1 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 159 | 3657 |
| 195 and 187 | 36465 |
| 136 and 157 | 21352 |
| 164 and 171 | 28044 |
| 70 and 66 | 2310 |