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 |
|---|---|
| 180 and 71 | 12780 |
| 60 and 23 | 1380 |
| 45 and 86 | 3870 |
| 196 and 114 | 11172 |
| 109 and 194 | 21146 |