Least Common Multiple (LCM) of 17 and 163
The least common multiple (LCM) of 17 and 163 is 2771.
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 163?
First, calculate the GCD of 17 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 163 = 0 remainder 17 |
| 2 | 163 ÷ 17 = 9 remainder 10 |
| 3 | 17 ÷ 10 = 1 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 60 | 4980 |
| 196 and 191 | 37436 |
| 42 and 34 | 714 |
| 83 and 75 | 6225 |
| 110 and 41 | 4510 |