Least Common Multiple (LCM) of 17 and 185
The least common multiple (LCM) of 17 and 185 is 3145.
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 185?
First, calculate the GCD of 17 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 185 = 0 remainder 17 |
| 2 | 185 ÷ 17 = 10 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 96 | 7392 |
| 104 and 46 | 2392 |
| 34 and 82 | 1394 |
| 65 and 85 | 1105 |
| 69 and 198 | 4554 |