Least Common Multiple (LCM) of 189 and 129
The least common multiple (LCM) of 189 and 129 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 189 and 129?
First, calculate the GCD of 189 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 129 = 1 remainder 60 |
| 2 | 129 ÷ 60 = 2 remainder 9 |
| 3 | 60 ÷ 9 = 6 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 15 | 1545 |
| 84 and 60 | 420 |
| 39 and 16 | 624 |
| 112 and 188 | 5264 |
| 173 and 78 | 13494 |