Least Common Multiple (LCM) of 125 and 192
The least common multiple (LCM) of 125 and 192 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 125 and 192?
First, calculate the GCD of 125 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 192 = 0 remainder 125 |
| 2 | 192 ÷ 125 = 1 remainder 67 |
| 3 | 125 ÷ 67 = 1 remainder 58 |
| 4 | 67 ÷ 58 = 1 remainder 9 |
| 5 | 58 ÷ 9 = 6 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 169 | 21632 |
| 54 and 115 | 6210 |
| 47 and 107 | 5029 |
| 56 and 64 | 448 |
| 83 and 71 | 5893 |