Least Common Multiple (LCM) of 112 and 82
The least common multiple (LCM) of 112 and 82 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 112 and 82?
First, calculate the GCD of 112 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 82 = 1 remainder 30 |
| 2 | 82 ÷ 30 = 2 remainder 22 |
| 3 | 30 ÷ 22 = 1 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 143 | 25740 |
| 133 and 89 | 11837 |
| 47 and 113 | 5311 |
| 59 and 51 | 3009 |
| 128 and 112 | 896 |