Least Common Multiple (LCM) of 111 and 194
The least common multiple (LCM) of 111 and 194 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 111 and 194?
First, calculate the GCD of 111 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 194 = 0 remainder 111 |
| 2 | 194 ÷ 111 = 1 remainder 83 |
| 3 | 111 ÷ 83 = 1 remainder 28 |
| 4 | 83 ÷ 28 = 2 remainder 27 |
| 5 | 28 ÷ 27 = 1 remainder 1 |
| 6 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 137 | 18084 |
| 74 and 75 | 5550 |
| 13 and 30 | 390 |
| 119 and 39 | 4641 |
| 90 and 194 | 8730 |