Least Common Multiple (LCM) of 189 and 144
The least common multiple (LCM) of 189 and 144 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 189 and 144?
First, calculate the GCD of 189 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 144 = 1 remainder 45 |
| 2 | 144 ÷ 45 = 3 remainder 9 |
| 3 | 45 ÷ 9 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 68 | 12036 |
| 138 and 102 | 2346 |
| 89 and 169 | 15041 |
| 61 and 124 | 7564 |
| 144 and 102 | 2448 |