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 |
|---|---|
| 162 and 26 | 2106 |
| 95 and 74 | 7030 |
| 171 and 139 | 23769 |
| 115 and 193 | 22195 |
| 90 and 171 | 1710 |