Least Common Multiple (LCM) of 192 and 103
The least common multiple (LCM) of 192 and 103 is 19776.
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 103?
First, calculate the GCD of 192 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 103 = 1 remainder 89 |
| 2 | 103 ÷ 89 = 1 remainder 14 |
| 3 | 89 ÷ 14 = 6 remainder 5 |
| 4 | 14 ÷ 5 = 2 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 198 | 21186 |
| 159 and 145 | 23055 |
| 109 and 10 | 1090 |
| 90 and 187 | 16830 |
| 174 and 111 | 6438 |