Least Common Multiple (LCM) of 198 and 131
The least common multiple (LCM) of 198 and 131 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 198 and 131?
First, calculate the GCD of 198 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 131 = 1 remainder 67 |
| 2 | 131 ÷ 67 = 1 remainder 64 |
| 3 | 67 ÷ 64 = 1 remainder 3 |
| 4 | 64 ÷ 3 = 21 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 75 | 2325 |
| 138 and 135 | 6210 |
| 50 and 19 | 950 |
| 73 and 59 | 4307 |
| 165 and 137 | 22605 |