Least Common Multiple (LCM) of 17 and 189
The least common multiple (LCM) of 17 and 189 is 3213.
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 189?
First, calculate the GCD of 17 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 189 = 0 remainder 17 |
| 2 | 189 ÷ 17 = 11 remainder 2 |
| 3 | 17 ÷ 2 = 8 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 187 | 32351 |
| 126 and 109 | 13734 |
| 185 and 89 | 16465 |
| 176 and 25 | 4400 |
| 157 and 166 | 26062 |