Least Common Multiple (LCM) of 131 and 198
The least common multiple (LCM) of 131 and 198 is 25938.
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 131 and 198?
First, calculate the GCD of 131 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 198 = 0 remainder 131 |
| 2 | 198 ÷ 131 = 1 remainder 67 |
| 3 | 131 ÷ 67 = 1 remainder 64 |
| 4 | 67 ÷ 64 = 1 remainder 3 |
| 5 | 64 ÷ 3 = 21 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 145 | 290 |
| 130 and 172 | 11180 |
| 161 and 42 | 966 |
| 77 and 28 | 308 |
| 127 and 80 | 10160 |