Least Common Multiple (LCM) of 192 and 107
The least common multiple (LCM) of 192 and 107 is 20544.
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 107?
First, calculate the GCD of 192 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 107 = 1 remainder 85 |
| 2 | 107 ÷ 85 = 1 remainder 22 |
| 3 | 85 ÷ 22 = 3 remainder 19 |
| 4 | 22 ÷ 19 = 1 remainder 3 |
| 5 | 19 ÷ 3 = 6 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 177 | 6195 |
| 122 and 153 | 18666 |
| 192 and 157 | 30144 |
| 134 and 164 | 10988 |
| 137 and 14 | 1918 |