Least Common Multiple (LCM) of 65 and 57
The least common multiple (LCM) of 65 and 57 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 65 and 57?
First, calculate the GCD of 65 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 57 = 1 remainder 8 |
| 2 | 57 ÷ 8 = 7 remainder 1 |
| 3 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 130 | 130 |
| 11 and 35 | 385 |
| 22 and 25 | 550 |
| 100 and 56 | 1400 |
| 164 and 83 | 13612 |