Least Common Multiple (LCM) of 41 and 199
The least common multiple (LCM) of 41 and 199 is 8159.
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 199?
First, calculate the GCD of 41 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 199 = 0 remainder 41 |
| 2 | 199 ÷ 41 = 4 remainder 35 |
| 3 | 41 ÷ 35 = 1 remainder 6 |
| 4 | 35 ÷ 6 = 5 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 180 | 1440 |
| 77 and 75 | 5775 |
| 160 and 143 | 22880 |
| 150 and 146 | 10950 |
| 200 and 23 | 4600 |