Least Common Multiple (LCM) of 129 and 186
The least common multiple (LCM) of 129 and 186 is 7998.
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 186?
First, calculate the GCD of 129 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 186 = 0 remainder 129 |
| 2 | 186 ÷ 129 = 1 remainder 57 |
| 3 | 129 ÷ 57 = 2 remainder 15 |
| 4 | 57 ÷ 15 = 3 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 49 | 980 |
| 71 and 109 | 7739 |
| 155 and 113 | 17515 |
| 15 and 121 | 1815 |
| 174 and 84 | 2436 |