Least Common Multiple (LCM) of 30 and 54
The least common multiple (LCM) of 30 and 54 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 30 and 54?
First, calculate the GCD of 30 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 54 = 0 remainder 30 |
| 2 | 54 ÷ 30 = 1 remainder 24 |
| 3 | 30 ÷ 24 = 1 remainder 6 |
| 4 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 86 | 5074 |
| 87 and 99 | 2871 |
| 47 and 122 | 5734 |
| 134 and 200 | 13400 |
| 22 and 103 | 2266 |