Least Common Multiple (LCM) of 57 and 199
The least common multiple (LCM) of 57 and 199 is 11343.
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 199?
First, calculate the GCD of 57 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 199 = 0 remainder 57 |
| 2 | 199 ÷ 57 = 3 remainder 28 |
| 3 | 57 ÷ 28 = 2 remainder 1 |
| 4 | 28 ÷ 1 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 39 | 2223 |
| 167 and 72 | 12024 |
| 21 and 122 | 2562 |
| 189 and 15 | 945 |
| 105 and 12 | 420 |