Least Common Multiple (LCM) of 57 and 200
The least common multiple (LCM) of 57 and 200 is 11400.
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 200?
First, calculate the GCD of 57 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 200 = 0 remainder 57 |
| 2 | 200 ÷ 57 = 3 remainder 29 |
| 3 | 57 ÷ 29 = 1 remainder 28 |
| 4 | 29 ÷ 28 = 1 remainder 1 |
| 5 | 28 ÷ 1 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 64 | 12224 |
| 115 and 138 | 690 |
| 62 and 14 | 434 |
| 17 and 113 | 1921 |
| 61 and 30 | 1830 |