Least Common Multiple (LCM) of 144 and 135
The least common multiple (LCM) of 144 and 135 is 2160.
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 144 and 135?
First, calculate the GCD of 144 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 135 = 1 remainder 9 |
| 2 | 135 ÷ 9 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 57 | 1311 |
| 22 and 78 | 858 |
| 135 and 137 | 18495 |
| 157 and 74 | 11618 |
| 190 and 62 | 5890 |