Least Common Multiple (LCM) of 18 and 33
The least common multiple (LCM) of 18 and 33 is 198.
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 18 and 33?
First, calculate the GCD of 18 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 33 = 0 remainder 18 |
| 2 | 33 ÷ 18 = 1 remainder 15 |
| 3 | 18 ÷ 15 = 1 remainder 3 |
| 4 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 46 | 5106 |
| 193 and 133 | 25669 |
| 48 and 73 | 3504 |
| 176 and 146 | 12848 |
| 32 and 132 | 1056 |