Least Common Multiple (LCM) of 82 and 138
The least common multiple (LCM) of 82 and 138 is 5658.
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 138?
First, calculate the GCD of 82 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 138 = 0 remainder 82 |
| 2 | 138 ÷ 82 = 1 remainder 56 |
| 3 | 82 ÷ 56 = 1 remainder 26 |
| 4 | 56 ÷ 26 = 2 remainder 4 |
| 5 | 26 ÷ 4 = 6 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 189 | 9450 |
| 31 and 85 | 2635 |
| 99 and 10 | 990 |
| 157 and 168 | 26376 |
| 14 and 99 | 1386 |