Least Common Multiple (LCM) of 106 and 197
The least common multiple (LCM) of 106 and 197 is 20882.
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 106 and 197?
First, calculate the GCD of 106 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 197 = 0 remainder 106 |
| 2 | 197 ÷ 106 = 1 remainder 91 |
| 3 | 106 ÷ 91 = 1 remainder 15 |
| 4 | 91 ÷ 15 = 6 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 87 | 9222 |
| 193 and 141 | 27213 |
| 199 and 159 | 31641 |
| 32 and 41 | 1312 |
| 116 and 145 | 580 |