Least Common Multiple (LCM) of 138 and 81
The least common multiple (LCM) of 138 and 81 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 138 and 81?
First, calculate the GCD of 138 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 81 = 1 remainder 57 |
| 2 | 81 ÷ 57 = 1 remainder 24 |
| 3 | 57 ÷ 24 = 2 remainder 9 |
| 4 | 24 ÷ 9 = 2 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 11 | 110 |
| 123 and 125 | 15375 |
| 47 and 13 | 611 |
| 33 and 77 | 231 |
| 198 and 187 | 3366 |