Least Common Multiple (LCM) of 82 and 143
The least common multiple (LCM) of 82 and 143 is 11726.
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 82 and 143?
First, calculate the GCD of 82 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 143 = 0 remainder 82 |
| 2 | 143 ÷ 82 = 1 remainder 61 |
| 3 | 82 ÷ 61 = 1 remainder 21 |
| 4 | 61 ÷ 21 = 2 remainder 19 |
| 5 | 21 ÷ 19 = 1 remainder 2 |
| 6 | 19 ÷ 2 = 9 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 85 | 4930 |
| 20 and 68 | 340 |
| 97 and 164 | 15908 |
| 25 and 197 | 4925 |
| 87 and 35 | 3045 |