Least Common Multiple (LCM) of 196 and 129
The least common multiple (LCM) of 196 and 129 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 196 and 129?
First, calculate the GCD of 196 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 129 = 1 remainder 67 |
| 2 | 129 ÷ 67 = 1 remainder 62 |
| 3 | 67 ÷ 62 = 1 remainder 5 |
| 4 | 62 ÷ 5 = 12 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 131 | 17423 |
| 163 and 105 | 17115 |
| 81 and 24 | 648 |
| 170 and 125 | 4250 |
| 192 and 137 | 26304 |