Least Common Multiple (LCM) of 54 and 30
The least common multiple (LCM) of 54 and 30 is 270.
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 54 and 30?
First, calculate the GCD of 54 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 30 = 1 remainder 24 |
| 2 | 30 ÷ 24 = 1 remainder 6 |
| 3 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 17 | 204 |
| 106 and 180 | 9540 |
| 185 and 97 | 17945 |
| 24 and 14 | 168 |
| 46 and 20 | 460 |