Least Common Multiple (LCM) of 105 and 81
The least common multiple (LCM) of 105 and 81 is 2835.
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 105 and 81?
First, calculate the GCD of 105 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 81 = 1 remainder 24 |
| 2 | 81 ÷ 24 = 3 remainder 9 |
| 3 | 24 ÷ 9 = 2 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 21 | 126 |
| 40 and 191 | 7640 |
| 37 and 197 | 7289 |
| 50 and 12 | 300 |
| 155 and 105 | 3255 |