Least Common Multiple (LCM) of 193 and 111
The least common multiple (LCM) of 193 and 111 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 193 and 111?
First, calculate the GCD of 193 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 111 = 1 remainder 82 |
| 2 | 111 ÷ 82 = 1 remainder 29 |
| 3 | 82 ÷ 29 = 2 remainder 24 |
| 4 | 29 ÷ 24 = 1 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 142 | 23998 |
| 51 and 191 | 9741 |
| 43 and 87 | 3741 |
| 15 and 161 | 2415 |
| 91 and 161 | 2093 |