Least Common Multiple (LCM) of 197 and 112
The least common multiple (LCM) of 197 and 112 is 22064.
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 197 and 112?
First, calculate the GCD of 197 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 112 = 1 remainder 85 |
| 2 | 112 ÷ 85 = 1 remainder 27 |
| 3 | 85 ÷ 27 = 3 remainder 4 |
| 4 | 27 ÷ 4 = 6 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 70 | 2730 |
| 83 and 27 | 2241 |
| 192 and 174 | 5568 |
| 133 and 29 | 3857 |
| 192 and 16 | 192 |