Least Common Multiple (LCM) of 108 and 193
The least common multiple (LCM) of 108 and 193 is 20844.
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 108 and 193?
First, calculate the GCD of 108 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 193 = 0 remainder 108 |
| 2 | 193 ÷ 108 = 1 remainder 85 |
| 3 | 108 ÷ 85 = 1 remainder 23 |
| 4 | 85 ÷ 23 = 3 remainder 16 |
| 5 | 23 ÷ 16 = 1 remainder 7 |
| 6 | 16 ÷ 7 = 2 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 137 | 25893 |
| 123 and 147 | 6027 |
| 173 and 100 | 17300 |
| 71 and 105 | 7455 |
| 163 and 123 | 20049 |