Least Common Multiple (LCM) of 144 and 189
The least common multiple (LCM) of 144 and 189 is 3024.
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 144 and 189?
First, calculate the GCD of 144 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 189 = 0 remainder 144 |
| 2 | 189 ÷ 144 = 1 remainder 45 |
| 3 | 144 ÷ 45 = 3 remainder 9 |
| 4 | 45 ÷ 9 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 85 | 3230 |
| 127 and 85 | 10795 |
| 50 and 159 | 7950 |
| 26 and 88 | 1144 |
| 173 and 117 | 20241 |