Least Common Multiple (LCM) of 82 and 104
The least common multiple (LCM) of 82 and 104 is 4264.
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 104?
First, calculate the GCD of 82 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 104 = 0 remainder 82 |
| 2 | 104 ÷ 82 = 1 remainder 22 |
| 3 | 82 ÷ 22 = 3 remainder 16 |
| 4 | 22 ÷ 16 = 1 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 56 | 7224 |
| 73 and 19 | 1387 |
| 106 and 155 | 16430 |
| 118 and 157 | 18526 |
| 173 and 122 | 21106 |