Least Common Multiple (LCM) of 41 and 17
The least common multiple (LCM) of 41 and 17 is 697.
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 17?
First, calculate the GCD of 41 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 41 ÷ 17 = 2 remainder 7 |
| 2 | 17 ÷ 7 = 2 remainder 3 |
| 3 | 7 ÷ 3 = 2 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 13 | 403 |
| 198 and 173 | 34254 |
| 137 and 133 | 18221 |
| 124 and 80 | 2480 |
| 149 and 104 | 15496 |