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 |
|---|---|
| 159 and 61 | 9699 |
| 59 and 25 | 1475 |
| 180 and 120 | 360 |
| 143 and 88 | 1144 |
| 147 and 17 | 2499 |