Least Common Multiple (LCM) of 129 and 196
The least common multiple (LCM) of 129 and 196 is 25284.
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 196?
First, calculate the GCD of 129 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 196 = 0 remainder 129 |
| 2 | 196 ÷ 129 = 1 remainder 67 |
| 3 | 129 ÷ 67 = 1 remainder 62 |
| 4 | 67 ÷ 62 = 1 remainder 5 |
| 5 | 62 ÷ 5 = 12 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 14 | 462 |
| 197 and 90 | 17730 |
| 187 and 86 | 16082 |
| 85 and 158 | 13430 |
| 20 and 194 | 1940 |