The product of two positive integers is $144$. The ratio of their least common multiple to their greatest common divisor is equal to $9$. What is the sum of the two integers?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The product of two positive integers is $144$. The ratio of their least common multiple to their greatest common divisor is equal to $9$. What is the sum of the two integers?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
40
The product of two positive integers is $144$. The ratio of their least common multiple to their greatest common divisor is equal to $9$. What is the sum of the two integers?
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