Least Common Multiple (LCM) of 81 and 109
The least common multiple (LCM) of 81 and 109 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 81 and 109?
First, calculate the GCD of 81 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 109 = 0 remainder 81 |
| 2 | 109 ÷ 81 = 1 remainder 28 |
| 3 | 81 ÷ 28 = 2 remainder 25 |
| 4 | 28 ÷ 25 = 1 remainder 3 |
| 5 | 25 ÷ 3 = 8 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 160 | 8480 |
| 152 and 31 | 4712 |
| 140 and 126 | 1260 |
| 61 and 186 | 11346 |
| 135 and 83 | 11205 |