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 |
|---|---|
| 111 and 65 | 7215 |
| 63 and 108 | 756 |
| 132 and 81 | 3564 |
| 114 and 125 | 14250 |
| 110 and 38 | 2090 |