Least Common Multiple (LCM) of 82 and 112
The least common multiple (LCM) of 82 and 112 is 4592.
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 112?
First, calculate the GCD of 82 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 112 = 0 remainder 82 |
| 2 | 112 ÷ 82 = 1 remainder 30 |
| 3 | 82 ÷ 30 = 2 remainder 22 |
| 4 | 30 ÷ 22 = 1 remainder 8 |
| 5 | 22 ÷ 8 = 2 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 74 | 11322 |
| 135 and 59 | 7965 |
| 78 and 27 | 702 |
| 87 and 84 | 2436 |
| 65 and 66 | 4290 |