Least Common Multiple (LCM) of 109 and 81
The least common multiple (LCM) of 109 and 81 is 8829.
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 109 and 81?
First, calculate the GCD of 109 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 81 = 1 remainder 28 |
| 2 | 81 ÷ 28 = 2 remainder 25 |
| 3 | 28 ÷ 25 = 1 remainder 3 |
| 4 | 25 ÷ 3 = 8 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 112 | 14448 |
| 77 and 120 | 9240 |
| 146 and 134 | 9782 |
| 91 and 81 | 7371 |
| 91 and 72 | 6552 |