Least Common Multiple (LCM) of 65 and 198
The least common multiple (LCM) of 65 and 198 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 65 and 198?
First, calculate the GCD of 65 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 198 = 0 remainder 65 |
| 2 | 198 ÷ 65 = 3 remainder 3 |
| 3 | 65 ÷ 3 = 21 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 105 | 3990 |
| 23 and 111 | 2553 |
| 165 and 91 | 15015 |
| 160 and 172 | 6880 |
| 157 and 129 | 20253 |