Least Common Multiple (LCM) of 82 and 31
The least common multiple (LCM) of 82 and 31 is 2542.
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 31?
First, calculate the GCD of 82 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 31 = 2 remainder 20 |
| 2 | 31 ÷ 20 = 1 remainder 11 |
| 3 | 20 ÷ 11 = 1 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 122 | 4880 |
| 129 and 166 | 21414 |
| 142 and 89 | 12638 |
| 53 and 127 | 6731 |
| 156 and 92 | 3588 |