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 |
|---|---|
| 109 and 185 | 20165 |
| 141 and 65 | 9165 |
| 178 and 94 | 8366 |
| 106 and 193 | 20458 |
| 147 and 18 | 882 |