Least Common Multiple (LCM) of 163 and 189
The least common multiple (LCM) of 163 and 189 is 30807.
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 163 and 189?
First, calculate the GCD of 163 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 189 = 0 remainder 163 |
| 2 | 189 ÷ 163 = 1 remainder 26 |
| 3 | 163 ÷ 26 = 6 remainder 7 |
| 4 | 26 ÷ 7 = 3 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 14 | 1610 |
| 105 and 14 | 210 |
| 180 and 176 | 7920 |
| 161 and 183 | 29463 |
| 144 and 106 | 7632 |