Least Common Multiple (LCM) of 82 and 106
The least common multiple (LCM) of 82 and 106 is 4346.
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 106?
First, calculate the GCD of 82 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 106 = 0 remainder 82 |
| 2 | 106 ÷ 82 = 1 remainder 24 |
| 3 | 82 ÷ 24 = 3 remainder 10 |
| 4 | 24 ÷ 10 = 2 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 100 | 4700 |
| 110 and 41 | 4510 |
| 174 and 103 | 17922 |
| 53 and 124 | 6572 |
| 114 and 120 | 2280 |