Least Common Multiple (LCM) of 129 and 197
The least common multiple (LCM) of 129 and 197 is 25413.
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 197?
First, calculate the GCD of 129 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 197 = 0 remainder 129 |
| 2 | 197 ÷ 129 = 1 remainder 68 |
| 3 | 129 ÷ 68 = 1 remainder 61 |
| 4 | 68 ÷ 61 = 1 remainder 7 |
| 5 | 61 ÷ 7 = 8 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 30 | 3090 |
| 25 and 54 | 1350 |
| 102 and 116 | 5916 |
| 177 and 79 | 13983 |
| 10 and 189 | 1890 |