Least Common Multiple (LCM) of 105 and 197
The least common multiple (LCM) of 105 and 197 is 20685.
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 105 and 197?
First, calculate the GCD of 105 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 197 = 0 remainder 105 |
| 2 | 197 ÷ 105 = 1 remainder 92 |
| 3 | 105 ÷ 92 = 1 remainder 13 |
| 4 | 92 ÷ 13 = 7 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 68 | 2244 |
| 109 and 140 | 15260 |
| 37 and 100 | 3700 |
| 156 and 101 | 15756 |
| 171 and 196 | 33516 |