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 |
|---|---|
| 175 and 72 | 12600 |
| 163 and 157 | 25591 |
| 165 and 111 | 6105 |
| 80 and 140 | 560 |
| 152 and 104 | 1976 |