Least Common Multiple (LCM) of 57 and 64
The least common multiple (LCM) of 57 and 64 is 3648.
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 64?
First, calculate the GCD of 57 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 64 = 0 remainder 57 |
| 2 | 64 ÷ 57 = 1 remainder 7 |
| 3 | 57 ÷ 7 = 8 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 136 | 16728 |
| 177 and 46 | 8142 |
| 17 and 148 | 2516 |
| 181 and 102 | 18462 |
| 189 and 90 | 1890 |