Least Common Multiple (LCM) of 57 and 65
The least common multiple (LCM) of 57 and 65 is 3705.
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 65?
First, calculate the GCD of 57 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 65 = 0 remainder 57 |
| 2 | 65 ÷ 57 = 1 remainder 8 |
| 3 | 57 ÷ 8 = 7 remainder 1 |
| 4 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 78 | 2262 |
| 128 and 179 | 22912 |
| 109 and 96 | 10464 |
| 99 and 194 | 19206 |
| 132 and 25 | 3300 |