Least Common Multiple (LCM) of 192 and 125
The least common multiple (LCM) of 192 and 125 is 24000.
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 125?
First, calculate the GCD of 192 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 125 = 1 remainder 67 |
| 2 | 125 ÷ 67 = 1 remainder 58 |
| 3 | 67 ÷ 58 = 1 remainder 9 |
| 4 | 58 ÷ 9 = 6 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 135 | 540 |
| 160 and 123 | 19680 |
| 196 and 50 | 4900 |
| 24 and 120 | 120 |
| 12 and 191 | 2292 |