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 |
|---|---|
| 32 and 72 | 288 |
| 72 and 139 | 10008 |
| 99 and 48 | 1584 |
| 126 and 185 | 23310 |
| 113 and 94 | 10622 |