Least Common Multiple (LCM) of 129 and 163
The least common multiple (LCM) of 129 and 163 is 21027.
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 163?
First, calculate the GCD of 129 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 163 = 0 remainder 129 |
| 2 | 163 ÷ 129 = 1 remainder 34 |
| 3 | 129 ÷ 34 = 3 remainder 27 |
| 4 | 34 ÷ 27 = 1 remainder 7 |
| 5 | 27 ÷ 7 = 3 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 10 | 20 |
| 188 and 132 | 6204 |
| 183 and 132 | 8052 |
| 189 and 55 | 10395 |
| 173 and 100 | 17300 |