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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?

Answer Choices

Yep! That's right.

Explanation

All numbers divisible by both 4 and 15 are the multiples of 4 and 15. Since 4 and 15 have no prime factor in common (4 = 2^2 comma 15 = 3 times 5), then the least common multiple of 4 and 15 is equal to their product, namely 4 times 15 = 60. Every other multiple of 4 and 15 is divisible by 60. Thus, if 60 is divisible by a number then all the multiples of 4 and 15 are divisible by that number. Therefore, it is enough to check by which number in the given options is 60 divisible. Only 6 divides 60 and none of the other do. The answer must be (A).

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