Least Common Multiple (LCM) of 112 and 83
The least common multiple (LCM) of 112 and 83 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 112 and 83?
First, calculate the GCD of 112 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 83 = 1 remainder 29 |
| 2 | 83 ÷ 29 = 2 remainder 25 |
| 3 | 29 ÷ 25 = 1 remainder 4 |
| 4 | 25 ÷ 4 = 6 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 117 | 18369 |
| 14 and 58 | 406 |
| 51 and 172 | 8772 |
| 120 and 49 | 5880 |
| 194 and 107 | 20758 |