Least Common Multiple (LCM) of 189 and 163
The least common multiple (LCM) of 189 and 163 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 189 and 163?
First, calculate the GCD of 189 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 163 = 1 remainder 26 |
| 2 | 163 ÷ 26 = 6 remainder 7 |
| 3 | 26 ÷ 7 = 3 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 119 | 7259 |
| 127 and 160 | 20320 |
| 121 and 128 | 15488 |
| 89 and 123 | 10947 |
| 60 and 26 | 780 |