Least Common Multiple (LCM) of 144 and 198
The least common multiple (LCM) of 144 and 198 is 1584.
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 198?
First, calculate the GCD of 144 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 198 = 0 remainder 144 |
| 2 | 198 ÷ 144 = 1 remainder 54 |
| 3 | 144 ÷ 54 = 2 remainder 36 |
| 4 | 54 ÷ 36 = 1 remainder 18 |
| 5 | 36 ÷ 18 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 196 | 392 |
| 64 and 46 | 1472 |
| 111 and 10 | 1110 |
| 42 and 164 | 3444 |
| 50 and 75 | 150 |