Least Common Multiple (LCM) of 189 and 195
The least common multiple (LCM) of 189 and 195 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 195?
First, calculate the GCD of 189 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 195 = 0 remainder 189 |
| 2 | 195 ÷ 189 = 1 remainder 6 |
| 3 | 189 ÷ 6 = 31 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 63 | 630 |
| 128 and 145 | 18560 |
| 193 and 36 | 6948 |
| 84 and 198 | 2772 |
| 141 and 91 | 12831 |