Least Common Multiple (LCM) of 97 and 197
The least common multiple (LCM) of 97 and 197 is 19109.
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 97 and 197?
First, calculate the GCD of 97 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 197 = 0 remainder 97 |
| 2 | 197 ÷ 97 = 2 remainder 3 |
| 3 | 97 ÷ 3 = 32 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 131 | 2358 |
| 105 and 63 | 315 |
| 126 and 74 | 4662 |
| 17 and 89 | 1513 |
| 132 and 126 | 2772 |