Least Common Multiple (LCM) of 189 and 170
The least common multiple (LCM) of 189 and 170 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 189 and 170?
First, calculate the GCD of 189 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 170 = 1 remainder 19 |
| 2 | 170 ÷ 19 = 8 remainder 18 |
| 3 | 19 ÷ 18 = 1 remainder 1 |
| 4 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 42 | 2310 |
| 169 and 64 | 10816 |
| 21 and 126 | 126 |
| 130 and 105 | 2730 |
| 10 and 193 | 1930 |