Find the smallest number that is completely divisible by both 42 and 78.

The correct option is D 546
The smallest number that is completely divisible by both 42 and 78 is the LCM of these two numbers.
We know, the prime factors of 42 and 78 are
42 = 2 $\times$ 3 $\times$ 7
78 = 2 $\times$ 3 $\times$ 13

The LCM of two or more given numbers is the lowest of their common multiples.

LCM (42, 78) = 2 $\times$ 3 $\times$ 7 $\times$ 13 = 546