Least Common Multiple (LCM) of 54 and 128
The least common multiple (LCM) of 54 and 128 is 3456.
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 54 and 128?
First, calculate the GCD of 54 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 128 = 0 remainder 54 |
| 2 | 128 ÷ 54 = 2 remainder 20 |
| 3 | 54 ÷ 20 = 2 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 30 | 1410 |
| 191 and 194 | 37054 |
| 41 and 123 | 123 |
| 97 and 39 | 3783 |
| 60 and 90 | 180 |