Least Common Multiple (LCM) of 57 and 80
The least common multiple (LCM) of 57 and 80 is 4560.
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 80?
First, calculate the GCD of 57 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 80 = 0 remainder 57 |
| 2 | 80 ÷ 57 = 1 remainder 23 |
| 3 | 57 ÷ 23 = 2 remainder 11 |
| 4 | 23 ÷ 11 = 2 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 84 | 2604 |
| 135 and 80 | 2160 |
| 90 and 133 | 11970 |
| 164 and 156 | 6396 |
| 174 and 109 | 18966 |