Least Common Multiple (LCM) of 111 and 193
The least common multiple (LCM) of 111 and 193 is 21423.
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 193?
First, calculate the GCD of 111 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 193 = 0 remainder 111 |
| 2 | 193 ÷ 111 = 1 remainder 82 |
| 3 | 111 ÷ 82 = 1 remainder 29 |
| 4 | 82 ÷ 29 = 2 remainder 24 |
| 5 | 29 ÷ 24 = 1 remainder 5 |
| 6 | 24 ÷ 5 = 4 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 45 | 2610 |
| 149 and 104 | 15496 |
| 100 and 57 | 5700 |
| 161 and 155 | 24955 |
| 43 and 142 | 6106 |