Least Common Multiple (LCM) of 135 and 144
The least common multiple (LCM) of 135 and 144 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 135 and 144?
First, calculate the GCD of 135 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 144 = 0 remainder 135 |
| 2 | 144 ÷ 135 = 1 remainder 9 |
| 3 | 135 ÷ 9 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 39 | 1638 |
| 85 and 42 | 3570 |
| 131 and 103 | 13493 |
| 122 and 92 | 5612 |
| 132 and 131 | 17292 |