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 |
|---|---|
| 130 and 69 | 8970 |
| 196 and 99 | 19404 |
| 102 and 13 | 1326 |
| 128 and 63 | 8064 |
| 88 and 90 | 3960 |