Least Common Multiple (LCM) of 81 and 138
The least common multiple (LCM) of 81 and 138 is 3726.
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 81 and 138?
First, calculate the GCD of 81 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 138 = 0 remainder 81 |
| 2 | 138 ÷ 81 = 1 remainder 57 |
| 3 | 81 ÷ 57 = 1 remainder 24 |
| 4 | 57 ÷ 24 = 2 remainder 9 |
| 5 | 24 ÷ 9 = 2 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 19 | 1425 |
| 142 and 192 | 13632 |
| 14 and 75 | 1050 |
| 158 and 49 | 7742 |
| 177 and 173 | 30621 |