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 |
|---|---|
| 112 and 15 | 1680 |
| 149 and 110 | 16390 |
| 157 and 183 | 28731 |
| 60 and 124 | 1860 |
| 146 and 135 | 19710 |