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 |
|---|---|
| 30 and 73 | 2190 |
| 180 and 118 | 10620 |
| 100 and 129 | 12900 |
| 148 and 67 | 9916 |
| 149 and 27 | 4023 |