Least Common Multiple (LCM) of 189 and 192
The least common multiple (LCM) of 189 and 192 is 12096.
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 192?
First, calculate the GCD of 189 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 192 = 0 remainder 189 |
| 2 | 192 ÷ 189 = 1 remainder 3 |
| 3 | 189 ÷ 3 = 63 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 176 | 11792 |
| 170 and 85 | 170 |
| 147 and 85 | 12495 |
| 110 and 75 | 1650 |
| 187 and 184 | 34408 |