Least Common Multiple (LCM) of 198 and 65
The least common multiple (LCM) of 198 and 65 is 12870.
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 198 and 65?
First, calculate the GCD of 198 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 65 = 3 remainder 3 |
| 2 | 65 ÷ 3 = 21 remainder 2 |
| 3 | 3 ÷ 2 = 1 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 99 | 1485 |
| 60 and 16 | 240 |
| 189 and 105 | 945 |
| 126 and 183 | 7686 |
| 105 and 119 | 1785 |