Suppose t is a positive integer such that lcm[12,t]^3=(6t)^3 . What is the smallest possible value for t?
+118609 Suppose t is a positive integer such that \(lcm[12,t]^3 = (6t)^3\) . What is the smallest possible value for t?
suppose the lowest common multiple is 12, (it can't be any smaller). This would be true if t=1,2,3,4,6, or 12
\(12^3=(6t)^3\\ (2*6)^3=6^3t^3\\ 2^3=t^2\\ t=2\)
The smallest value of t is 2
