Least Common Multiple (LCM) of 197 and 129
The least common multiple (LCM) of 197 and 129 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 197 and 129?
First, calculate the GCD of 197 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 129 = 1 remainder 68 |
| 2 | 129 ÷ 68 = 1 remainder 61 |
| 3 | 68 ÷ 61 = 1 remainder 7 |
| 4 | 61 ÷ 7 = 8 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 100 | 6100 |
| 101 and 189 | 19089 |
| 197 and 155 | 30535 |
| 170 and 115 | 3910 |
| 81 and 104 | 8424 |