Least Common Multiple (LCM) of 57 and 194
The least common multiple (LCM) of 57 and 194 is 11058.
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 194?
First, calculate the GCD of 57 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 194 = 0 remainder 57 |
| 2 | 194 ÷ 57 = 3 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 |
|---|---|
| 13 and 144 | 1872 |
| 130 and 129 | 16770 |
| 174 and 19 | 3306 |
| 196 and 35 | 980 |
| 34 and 152 | 2584 |