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 |
|---|---|
| 195 and 43 | 8385 |
| 128 and 105 | 13440 |
| 43 and 31 | 1333 |
| 189 and 52 | 9828 |
| 110 and 144 | 7920 |