Least Common Multiple (LCM) of 194 and 111
The least common multiple (LCM) of 194 and 111 is 21534.
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 194 and 111?
First, calculate the GCD of 194 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 111 = 1 remainder 83 |
| 2 | 111 ÷ 83 = 1 remainder 28 |
| 3 | 83 ÷ 28 = 2 remainder 27 |
| 4 | 28 ÷ 27 = 1 remainder 1 |
| 5 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 11 | 1397 |
| 162 and 159 | 8586 |
| 191 and 182 | 34762 |
| 164 and 82 | 164 |
| 174 and 162 | 4698 |