Least Common Multiple (LCM) of 57 and 197
The least common multiple (LCM) of 57 and 197 is 11229.
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 197?
First, calculate the GCD of 57 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 197 = 0 remainder 57 |
| 2 | 197 ÷ 57 = 3 remainder 26 |
| 3 | 57 ÷ 26 = 2 remainder 5 |
| 4 | 26 ÷ 5 = 5 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 112 | 1232 |
| 144 and 45 | 720 |
| 119 and 139 | 16541 |
| 83 and 126 | 10458 |
| 92 and 89 | 8188 |