What is the least common multiple of t and v if the greatest common factor of t and v is 8?
A) t
B) v
C) t + v
D) $\frac { tv } { 8 }$
E) none of these

Question

Quizplus · Accepted Answer

Let t = 8a and v = 8b, where a and b are positive integers. 
Then the least common multiple (LCM) of t and v can be expressed as LCM(t,v) = 8ab. 
Therefore, LCM(t,v) = (8a)(8b) = 8(t)(v)/8, 
which simplifies to LCM(t,v) = tv/8. 
Thus, the least common multiple of t and v is tv/8, which is answer choice D.

What Is the Least Common Multiple of T and V tv8\frac { tv } { 8 }8tv​

What Is the Least Common Multiple of T and V $\frac { tv } { 8 }$