Least Common Multiple (LCM) of 77 and 128
The least common multiple (LCM) of 77 and 128 is 9856.
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 77 and 128?
First, calculate the GCD of 77 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 128 = 0 remainder 77 |
| 2 | 128 ÷ 77 = 1 remainder 51 |
| 3 | 77 ÷ 51 = 1 remainder 26 |
| 4 | 51 ÷ 26 = 1 remainder 25 |
| 5 | 26 ÷ 25 = 1 remainder 1 |
| 6 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 31 | 6138 |
| 42 and 64 | 1344 |
| 40 and 25 | 200 |
| 31 and 74 | 2294 |
| 107 and 11 | 1177 |