Least Common Multiple (LCM) of 83 and 112
The least common multiple (LCM) of 83 and 112 is 9296.
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 83 and 112?
First, calculate the GCD of 83 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 112 = 0 remainder 83 |
| 2 | 112 ÷ 83 = 1 remainder 29 |
| 3 | 83 ÷ 29 = 2 remainder 25 |
| 4 | 29 ÷ 25 = 1 remainder 4 |
| 5 | 25 ÷ 4 = 6 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 20 | 3660 |
| 193 and 28 | 5404 |
| 159 and 186 | 9858 |
| 83 and 98 | 8134 |
| 156 and 32 | 1248 |