Least Common Multiple (LCM) of 17 and 82
The least common multiple (LCM) of 17 and 82 is 1394.
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 82?
First, calculate the GCD of 17 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 82 = 0 remainder 17 |
| 2 | 82 ÷ 17 = 4 remainder 14 |
| 3 | 17 ÷ 14 = 1 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 199 | 31243 |
| 25 and 165 | 825 |
| 39 and 142 | 5538 |
| 150 and 160 | 2400 |
| 21 and 126 | 126 |