Least Common Multiple (LCM) of 129 and 61
The least common multiple (LCM) of 129 and 61 is 7869.
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 61?
First, calculate the GCD of 129 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 61 = 2 remainder 7 |
| 2 | 61 ÷ 7 = 8 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 29 | 3248 |
| 12 and 198 | 396 |
| 76 and 163 | 12388 |
| 64 and 17 | 1088 |
| 172 and 61 | 10492 |