Least Common Multiple (LCM) of 109 and 82
The least common multiple (LCM) of 109 and 82 is 8938.
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 82?
First, calculate the GCD of 109 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 82 = 1 remainder 27 |
| 2 | 82 ÷ 27 = 3 remainder 1 |
| 3 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 105 | 2310 |
| 71 and 45 | 3195 |
| 161 and 96 | 15456 |
| 72 and 110 | 3960 |
| 99 and 72 | 792 |