Least Common Multiple (LCM) of 164 and 189
The least common multiple (LCM) of 164 and 189 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 164 and 189?
First, calculate the GCD of 164 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 189 = 0 remainder 164 |
| 2 | 189 ÷ 164 = 1 remainder 25 |
| 3 | 164 ÷ 25 = 6 remainder 14 |
| 4 | 25 ÷ 14 = 1 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 181 | 20091 |
| 14 and 82 | 574 |
| 113 and 135 | 15255 |
| 35 and 137 | 4795 |
| 119 and 45 | 5355 |