Least Common Multiple (LCM) of 33 and 18
The least common multiple (LCM) of 33 and 18 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 33 and 18?
First, calculate the GCD of 33 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 18 = 1 remainder 15 |
| 2 | 18 ÷ 15 = 1 remainder 3 |
| 3 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 186 | 3534 |
| 129 and 160 | 20640 |
| 180 and 10 | 180 |
| 149 and 99 | 14751 |
| 27 and 107 | 2889 |