Least Common Multiple (LCM) of 78 and 128
The least common multiple (LCM) of 78 and 128 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 78 and 128?
First, calculate the GCD of 78 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 128 = 0 remainder 78 |
| 2 | 128 ÷ 78 = 1 remainder 50 |
| 3 | 78 ÷ 50 = 1 remainder 28 |
| 4 | 50 ÷ 28 = 1 remainder 22 |
| 5 | 28 ÷ 22 = 1 remainder 6 |
| 6 | 22 ÷ 6 = 3 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 45 | 450 |
| 126 and 16 | 1008 |
| 107 and 114 | 12198 |
| 189 and 44 | 8316 |
| 55 and 161 | 8855 |