Least Common Multiple (LCM) of 33 and 108
The least common multiple (LCM) of 33 and 108 is 1188.
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 108?
First, calculate the GCD of 33 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 108 = 0 remainder 33 |
| 2 | 108 ÷ 33 = 3 remainder 9 |
| 3 | 33 ÷ 9 = 3 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 128 | 15488 |
| 75 and 108 | 2700 |
| 65 and 106 | 6890 |
| 34 and 121 | 4114 |
| 130 and 25 | 650 |