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a number is 6.

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 = 22, 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).

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Q: All numbers divisible by both 4 and 15 are also divisible by what numbers?
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Are all even numbers divisible by 6?

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What are the common multiples of 2 and 5?

The common multiples of 2 and 5 are 10, 20, 30, 40, etc.In detail:A common multiple is a number divisible by both (or all) numbers: 2 and 5, here.Knowing that all numbers divisible by 2 have a 0, 2, 4, 6, or 8 in the ones place combined with the knowledge that all numbers divisible by 5 end with 0 or 5 (excluding 0 in both cases), we can say the only multiples of each number that are common to both are numbers that end with 0.Another way of analyzing this problem is to say that both 5 and 2 are factors. 10 is clearly a multiple of 5 and 2 because 2(5)=10. Any number divisible by 10 is thus also divisible by 2 and 5. All numbers divisible by 10 end in 0. Thus, a number ends in 0 if and only if it is divisible by 2 and 5.Answer: Common multiples of 2 and 5 end with zero.