Least Common Multiple (LCM) of 17 and 118
The least common multiple (LCM) of 17 and 118 is 2006.
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 118?
First, calculate the GCD of 17 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 118 = 0 remainder 17 |
| 2 | 118 ÷ 17 = 6 remainder 16 |
| 3 | 17 ÷ 16 = 1 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 65 | 4355 |
| 25 and 103 | 2575 |
| 170 and 199 | 33830 |
| 186 and 111 | 6882 |
| 147 and 80 | 11760 |