Least Common Multiple (LCM) of 192 and 189
The least common multiple (LCM) of 192 and 189 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 192 and 189?
First, calculate the GCD of 192 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 189 = 1 remainder 3 |
| 2 | 189 ÷ 3 = 63 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 34 | 680 |
| 185 and 27 | 4995 |
| 123 and 166 | 20418 |
| 144 and 108 | 432 |
| 102 and 49 | 4998 |