
Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
All numbers divisible by both 4 and 15 are also divisible by which of the following?
(A) 6
(B) 8
(C) 18
(D) 24
(E) 45
The correct answer is C
Explanation
All numbers divisible by both
and
are the multiples of
and
. Since
and
have no prime factor in common
, then the least common multiple of
and
is equal to their product, namely
. Every other multiple of
and
is divisible by
. Thus, if
is divisible by a number then all the multiples of
and
are divisible by that number. Therefore, it is enough to check by which number in the given options is
divisible. Only
divides
and none of the other do. The answer must be
.