Least Common Multiple (LCM) of 189 and 164
The least common multiple (LCM) of 189 and 164 is 30996.
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 164?
First, calculate the GCD of 189 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 164 = 1 remainder 25 |
| 2 | 164 ÷ 25 = 6 remainder 14 |
| 3 | 25 ÷ 14 = 1 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 164 | 16236 |
| 46 and 117 | 5382 |
| 91 and 135 | 12285 |
| 24 and 73 | 1752 |
| 85 and 191 | 16235 |