Least Common Multiple (LCM) of 129 and 77
The least common multiple (LCM) of 129 and 77 is 9933.
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 77?
First, calculate the GCD of 129 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 77 = 1 remainder 52 |
| 2 | 77 ÷ 52 = 1 remainder 25 |
| 3 | 52 ÷ 25 = 2 remainder 2 |
| 4 | 25 ÷ 2 = 12 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 65 | 4680 |
| 65 and 97 | 6305 |
| 16 and 76 | 304 |
| 57 and 153 | 2907 |
| 107 and 123 | 13161 |