Least Common Multiple (LCM) of 65 and 193
The least common multiple (LCM) of 65 and 193 is 12545.
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 65 and 193?
First, calculate the GCD of 65 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 193 = 0 remainder 65 |
| 2 | 193 ÷ 65 = 2 remainder 63 |
| 3 | 65 ÷ 63 = 1 remainder 2 |
| 4 | 63 ÷ 2 = 31 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 40 | 1080 |
| 132 and 128 | 4224 |
| 174 and 54 | 1566 |
| 133 and 168 | 3192 |
| 134 and 58 | 3886 |