Least Common Multiple (LCM) of 65 and 189
The least common multiple (LCM) of 65 and 189 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 65 and 189?
First, calculate the GCD of 65 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 189 = 0 remainder 65 |
| 2 | 189 ÷ 65 = 2 remainder 59 |
| 3 | 65 ÷ 59 = 1 remainder 6 |
| 4 | 59 ÷ 6 = 9 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 195 | 7215 |
| 38 and 77 | 2926 |
| 144 and 116 | 4176 |
| 40 and 56 | 280 |
| 123 and 30 | 1230 |