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 |
|---|---|
| 132 and 109 | 14388 |
| 40 and 170 | 680 |
| 98 and 24 | 1176 |
| 118 and 181 | 21358 |
| 147 and 22 | 3234 |