Least Common Multiple (LCM) of 82 and 54
The least common multiple (LCM) of 82 and 54 is 2214.
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 54?
First, calculate the GCD of 82 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 54 = 1 remainder 28 |
| 2 | 54 ÷ 28 = 1 remainder 26 |
| 3 | 28 ÷ 26 = 1 remainder 2 |
| 4 | 26 ÷ 2 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 83 | 10209 |
| 125 and 150 | 750 |
| 148 and 63 | 9324 |
| 186 and 196 | 18228 |
| 13 and 113 | 1469 |