Least Common Multiple (LCM) of 144 and 33
The least common multiple (LCM) of 144 and 33 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 33?
First, calculate the GCD of 144 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 33 = 4 remainder 12 |
| 2 | 33 ÷ 12 = 2 remainder 9 |
| 3 | 12 ÷ 9 = 1 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 69 | 3381 |
| 101 and 71 | 7171 |
| 199 and 95 | 18905 |
| 108 and 86 | 4644 |
| 20 and 177 | 3540 |