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 |
|---|---|
| 110 and 166 | 9130 |
| 100 and 125 | 500 |
| 168 and 112 | 336 |
| 178 and 75 | 13350 |
| 169 and 132 | 22308 |