Least Common Multiple (LCM) of 128 and 78
The least common multiple (LCM) of 128 and 78 is 4992.
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 128 and 78?
First, calculate the GCD of 128 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 78 = 1 remainder 50 |
| 2 | 78 ÷ 50 = 1 remainder 28 |
| 3 | 50 ÷ 28 = 1 remainder 22 |
| 4 | 28 ÷ 22 = 1 remainder 6 |
| 5 | 22 ÷ 6 = 3 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 99 | 13464 |
| 94 and 177 | 16638 |
| 187 and 46 | 8602 |
| 54 and 60 | 540 |
| 163 and 192 | 31296 |