Least Common Multiple (LCM) of 82 and 128
The least common multiple (LCM) of 82 and 128 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 82 and 128?
First, calculate the GCD of 82 and 128 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 128 = 0 remainder 82 |
| 2 | 128 ÷ 82 = 1 remainder 46 |
| 3 | 82 ÷ 46 = 1 remainder 36 |
| 4 | 46 ÷ 36 = 1 remainder 10 |
| 5 | 36 ÷ 10 = 3 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 194 | 10282 |
| 36 and 37 | 1332 |
| 111 and 129 | 4773 |
| 174 and 170 | 14790 |
| 100 and 177 | 17700 |