Least Common Multiple (LCM) of 106 and 192
The least common multiple (LCM) of 106 and 192 is 10176.
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 106 and 192?
First, calculate the GCD of 106 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 192 = 0 remainder 106 |
| 2 | 192 ÷ 106 = 1 remainder 86 |
| 3 | 106 ÷ 86 = 1 remainder 20 |
| 4 | 86 ÷ 20 = 4 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 122 | 5002 |
| 183 and 123 | 7503 |
| 31 and 75 | 2325 |
| 127 and 116 | 14732 |
| 20 and 95 | 380 |