Least Common Multiple (LCM) of 82 and 109
The least common multiple (LCM) of 82 and 109 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 82 and 109?
First, calculate the GCD of 82 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 109 = 0 remainder 82 |
| 2 | 109 ÷ 82 = 1 remainder 27 |
| 3 | 82 ÷ 27 = 3 remainder 1 |
| 4 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 84 | 13020 |
| 184 and 17 | 3128 |
| 138 and 124 | 8556 |
| 183 and 18 | 1098 |
| 197 and 32 | 6304 |