Suppose $t$ is a positive integer such that $\mathop{\text{lcm}}[12,t]^3=(12t)^2$. What is the smallest possible value for $t$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Suppose $t$ is a positive integer such that $\mathop{\text{lcm}}[12,t]^3=(12t)^2$. What is the smallest possible value for $t$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
18
Suppose $t$ is a positive integer such that $\mathop{\text{lcm}}[12,t]^3=(12t)^2$. What is the smallest possible value for $t$?
train