答案：A

解析：

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 , 15 = 3*5), then the least common multiple of 4 and 15 is equal to their product, namely 4*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).