Least Common Multiple (LCM) of 81 and 38
The least common multiple (LCM) of 81 and 38 is 3078.
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 38?
First, calculate the GCD of 81 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 38 = 2 remainder 5 |
| 2 | 38 ÷ 5 = 7 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 31 | 4929 |
| 137 and 40 | 5480 |
| 131 and 107 | 14017 |
| 129 and 81 | 3483 |
| 180 and 54 | 540 |