Least Common Multiple (LCM) of 192 and 106
The least common multiple (LCM) of 192 and 106 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 192 and 106?
First, calculate the GCD of 192 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 106 = 1 remainder 86 |
| 2 | 106 ÷ 86 = 1 remainder 20 |
| 3 | 86 ÷ 20 = 4 remainder 6 |
| 4 | 20 ÷ 6 = 3 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 114 | 114 |
| 33 and 16 | 528 |
| 116 and 173 | 20068 |
| 152 and 185 | 28120 |
| 10 and 102 | 510 |