Least Common Multiple (LCM) of 129 and 68
The least common multiple (LCM) of 129 and 68 is 8772.
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 68?
First, calculate the GCD of 129 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 68 = 1 remainder 61 |
| 2 | 68 ÷ 61 = 1 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 |
|---|---|
| 108 and 178 | 9612 |
| 40 and 127 | 5080 |
| 72 and 34 | 1224 |
| 109 and 165 | 17985 |
| 60 and 11 | 660 |