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 |
|---|---|
| 137 and 111 | 15207 |
| 63 and 144 | 1008 |
| 48 and 184 | 1104 |
| 96 and 157 | 15072 |
| 92 and 97 | 8924 |