Least Common Multiple (LCM) of 57 and 128
The least common multiple (LCM) of 57 and 128 is 7296.
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 57 and 128?
First, calculate the GCD of 57 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 128 = 0 remainder 57 |
| 2 | 128 ÷ 57 = 2 remainder 14 |
| 3 | 57 ÷ 14 = 4 remainder 1 |
| 4 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 113 | 4859 |
| 119 and 99 | 11781 |
| 175 and 18 | 3150 |
| 184 and 189 | 34776 |
| 54 and 80 | 2160 |