Least Common Multiple (LCM) of 130 and 197
The least common multiple (LCM) of 130 and 197 is 25610.
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 130 and 197?
First, calculate the GCD of 130 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 197 = 0 remainder 130 |
| 2 | 197 ÷ 130 = 1 remainder 67 |
| 3 | 130 ÷ 67 = 1 remainder 63 |
| 4 | 67 ÷ 63 = 1 remainder 4 |
| 5 | 63 ÷ 4 = 15 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 68 | 2856 |
| 21 and 140 | 420 |
| 34 and 157 | 5338 |
| 170 and 66 | 5610 |
| 84 and 82 | 3444 |