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 |
|---|---|
| 37 and 111 | 111 |
| 111 and 83 | 9213 |
| 50 and 169 | 8450 |
| 165 and 16 | 2640 |
| 140 and 56 | 280 |