If $a, b$ and $c$ are positive integers with $a \times b=13, b \times c=52$, and $c \times a=4$, the value of $a \times b \times c$ is
(A) 2704
(B) 104
(C) 676
(D) 208
(E) 52
If $a$ and $b$ are positive integers with $a \times b=13$, then since 13 is a prime number, we must have $a$ and $b$ equal to 1 and 13 , or 13 and 1 , respectively.

If $b=1$, then since $b \times c=52$, we must have $c=52$. But then we could not have $c \times a=4$. So $b$ cannot be 1 .

Thus, $b=13$, so $a=1$, and $c=4$ (which we can get either from knowing $b=13$ and $b \times c=52$, or from knowing $a=1$ and $c \times a=4$.

Therefore, $a \times b \times c=1 \times 13 \times 4=52$.

ANSWER: (E)

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