Least Common Multiple (LCM) of 66 and 193
The least common multiple (LCM) of 66 and 193 is 12738.
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 66 and 193?
First, calculate the GCD of 66 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 193 = 0 remainder 66 |
| 2 | 193 ÷ 66 = 2 remainder 61 |
| 3 | 66 ÷ 61 = 1 remainder 5 |
| 4 | 61 ÷ 5 = 12 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 192 | 19776 |
| 197 and 82 | 16154 |
| 111 and 83 | 9213 |
| 135 and 149 | 20115 |
| 178 and 26 | 2314 |