Least Common Multiple (LCM) of 17 and 192
The least common multiple (LCM) of 17 and 192 is 3264.
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 17 and 192?
First, calculate the GCD of 17 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 192 = 0 remainder 17 |
| 2 | 192 ÷ 17 = 11 remainder 5 |
| 3 | 17 ÷ 5 = 3 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 16 | 784 |
| 103 and 178 | 18334 |
| 184 and 177 | 32568 |
| 92 and 10 | 460 |
| 74 and 69 | 5106 |