Least Common Multiple (LCM) of 129 and 189
The least common multiple (LCM) of 129 and 189 is 8127.
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 189?
First, calculate the GCD of 129 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 189 = 0 remainder 129 |
| 2 | 189 ÷ 129 = 1 remainder 60 |
| 3 | 129 ÷ 60 = 2 remainder 9 |
| 4 | 60 ÷ 9 = 6 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 18 | 198 |
| 109 and 30 | 3270 |
| 102 and 134 | 6834 |
| 194 and 44 | 4268 |
| 38 and 175 | 6650 |