Least Common Multiple (LCM) of 189 and 65
The least common multiple (LCM) of 189 and 65 is 12285.
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 189 and 65?
First, calculate the GCD of 189 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 65 = 2 remainder 59 |
| 2 | 65 ÷ 59 = 1 remainder 6 |
| 3 | 59 ÷ 6 = 9 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 133 | 798 |
| 65 and 15 | 195 |
| 199 and 66 | 13134 |
| 158 and 49 | 7742 |
| 54 and 10 | 270 |