Least Common Multiple (LCM) of 61 and 129
The least common multiple (LCM) of 61 and 129 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 61 and 129?
First, calculate the GCD of 61 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 129 = 0 remainder 61 |
| 2 | 129 ÷ 61 = 2 remainder 7 |
| 3 | 61 ÷ 7 = 8 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 19 | 190 |
| 69 and 58 | 4002 |
| 116 and 133 | 15428 |
| 100 and 73 | 7300 |
| 77 and 193 | 14861 |