Least Common Multiple (LCM) of 193 and 118
The least common multiple (LCM) of 193 and 118 is 22774.
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 118?
First, calculate the GCD of 193 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 118 = 1 remainder 75 |
| 2 | 118 ÷ 75 = 1 remainder 43 |
| 3 | 75 ÷ 43 = 1 remainder 32 |
| 4 | 43 ÷ 32 = 1 remainder 11 |
| 5 | 32 ÷ 11 = 2 remainder 10 |
| 6 | 11 ÷ 10 = 1 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 86 | 774 |
| 107 and 181 | 19367 |
| 134 and 199 | 26666 |
| 199 and 95 | 18905 |
| 123 and 45 | 1845 |