Least Common Multiple (LCM) of 128 and 82
The least common multiple (LCM) of 128 and 82 is 5248.
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 128 and 82?
First, calculate the GCD of 128 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 82 = 1 remainder 46 |
| 2 | 82 ÷ 46 = 1 remainder 36 |
| 3 | 46 ÷ 36 = 1 remainder 10 |
| 4 | 36 ÷ 10 = 3 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 148 | 8140 |
| 17 and 27 | 459 |
| 103 and 180 | 18540 |
| 169 and 154 | 26026 |
| 17 and 37 | 629 |