Least Common Multiple (LCM) of 112 and 163
The least common multiple (LCM) of 112 and 163 is 18256.
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 163?
First, calculate the GCD of 112 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 163 = 0 remainder 112 |
| 2 | 163 ÷ 112 = 1 remainder 51 |
| 3 | 112 ÷ 51 = 2 remainder 10 |
| 4 | 51 ÷ 10 = 5 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 127 | 17653 |
| 196 and 194 | 19012 |
| 98 and 106 | 5194 |
| 132 and 142 | 9372 |
| 14 and 179 | 2506 |