Find the LCM of $90,128,$ and $144$.

Let's find the prime factorization of each number:
* $90=2\times 3^2\times 5=2^1\times 3^2\times 5^1$
* $128=2^7$
* $144=12^2=(2^2\times 3{)}^2=2^4\times 3^2$

To find the Least Common Multiple (LCM), we take the highest power of each prime number present across the numbers:

* Highest power of 2: $2^7=128$
* Highest power of 3: $3^2=9$
* Highest power of 5: $5^1=5$

Now, multiply these values together:

$$\text{LCM}=2^7\times 3^2\times 5^1$$

$$\text{LCM}=128\times 9\times 5$$

$$\text{LCM}=128\times 45=5760$$