Least Common Multiple (LCM) of 170 and 189
The least common multiple (LCM) of 170 and 189 is 32130.
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 170 and 189?
First, calculate the GCD of 170 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 189 = 0 remainder 170 |
| 2 | 189 ÷ 170 = 1 remainder 19 |
| 3 | 170 ÷ 19 = 8 remainder 18 |
| 4 | 19 ÷ 18 = 1 remainder 1 |
| 5 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 111 | 6549 |
| 164 and 127 | 20828 |
| 14 and 50 | 350 |
| 86 and 91 | 7826 |
| 101 and 198 | 19998 |