Least Common Multiple (LCM) of 108 and 81
The least common multiple (LCM) of 108 and 81 is 324.
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 108 and 81?
First, calculate the GCD of 108 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 81 = 1 remainder 27 |
| 2 | 81 ÷ 27 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 142 | 14342 |
| 100 and 55 | 1100 |
| 67 and 33 | 2211 |
| 197 and 72 | 14184 |
| 61 and 39 | 2379 |