Least Common Multiple (LCM) of 111 and 163
The least common multiple (LCM) of 111 and 163 is 18093.
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 163?
First, calculate the GCD of 111 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 163 = 0 remainder 111 |
| 2 | 163 ÷ 111 = 1 remainder 52 |
| 3 | 111 ÷ 52 = 2 remainder 7 |
| 4 | 52 ÷ 7 = 7 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 193 | 10808 |
| 54 and 69 | 1242 |
| 15 and 105 | 105 |
| 92 and 74 | 3404 |
| 92 and 187 | 17204 |