Least Common Multiple (LCM) of 41 and 198
The least common multiple (LCM) of 41 and 198 is 8118.
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 41 and 198?
First, calculate the GCD of 41 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 198 = 0 remainder 41 |
| 2 | 198 ÷ 41 = 4 remainder 34 |
| 3 | 41 ÷ 34 = 1 remainder 7 |
| 4 | 34 ÷ 7 = 4 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 49 | 8820 |
| 41 and 102 | 4182 |
| 96 and 10 | 480 |
| 177 and 159 | 9381 |
| 158 and 157 | 24806 |