Least Common Multiple (LCM) of 111 and 81
The least common multiple (LCM) of 111 and 81 is 2997.
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 111 and 81?
First, calculate the GCD of 111 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 81 = 1 remainder 30 |
| 2 | 81 ÷ 30 = 2 remainder 21 |
| 3 | 30 ÷ 21 = 1 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 46 | 2438 |
| 36 and 144 | 144 |
| 93 and 195 | 6045 |
| 110 and 21 | 2310 |
| 39 and 128 | 4992 |