Least Common Multiple (LCM) of 82 and 131
The least common multiple (LCM) of 82 and 131 is 10742.
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 131?
First, calculate the GCD of 82 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 131 = 0 remainder 82 |
| 2 | 131 ÷ 82 = 1 remainder 49 |
| 3 | 82 ÷ 49 = 1 remainder 33 |
| 4 | 49 ÷ 33 = 1 remainder 16 |
| 5 | 33 ÷ 16 = 2 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 22 | 2134 |
| 36 and 71 | 2556 |
| 102 and 93 | 3162 |
| 104 and 142 | 7384 |
| 56 and 199 | 11144 |