Least Common Multiple (LCM) of 135 and 54
The least common multiple (LCM) of 135 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 135 and 54?
First, calculate the GCD of 135 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 54 = 2 remainder 27 |
| 2 | 54 ÷ 27 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 117 | 2223 |
| 23 and 99 | 2277 |
| 122 and 75 | 9150 |
| 33 and 21 | 231 |
| 186 and 14 | 1302 |