Least Common Multiple (LCM) of 138 and 82
The least common multiple (LCM) of 138 and 82 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 138 and 82?
First, calculate the GCD of 138 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 82 = 1 remainder 56 |
| 2 | 82 ÷ 56 = 1 remainder 26 |
| 3 | 56 ÷ 26 = 2 remainder 4 |
| 4 | 26 ÷ 4 = 6 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 169 | 845 |
| 162 and 116 | 9396 |
| 20 and 122 | 1220 |
| 126 and 149 | 18774 |
| 172 and 45 | 7740 |