Least Common Multiple (LCM) of 17 and 41
The least common multiple (LCM) of 17 and 41 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 17 and 41?
First, calculate the GCD of 17 and 41 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 41 = 0 remainder 17 |
| 2 | 41 ÷ 17 = 2 remainder 7 |
| 3 | 17 ÷ 7 = 2 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 50 | 3100 |
| 135 and 77 | 10395 |
| 62 and 126 | 3906 |
| 37 and 114 | 4218 |
| 60 and 46 | 1380 |