common multiple

[Pra4ash]

Hi all! i just don't get the following question. The answer however is 3 and 6

Which of the following pairs of numbers has the most number of common multiples which are less than 30?
(a) 3 and 4
(b) 3 and 5
(c) 3 and 6
(d) 4 and 6

Thanks guys.

Pra4ash​

 

[MarkFL]

Since 6 is a multiple of 3, then all of the multiples of 6 will also be multiples of 3. There are 4 multiples of 6 less than 30.

You want to look at the LCM of each pair, and the pair with the smallest LCM will have the most number of common multiples which are less than some number greater than the largest LCM.

LCM(3,4) = 12

LCM(3,5) = 15

LCM(3,6) = 6

LCM(4,6) = 12

 

[Pra4ash]

Since 6 is a multiple of 3, then all of the multiples of 6 will also be multiples of 3. There are 4 multiples of 6 less than 30.

You want to look at the LCM of each pair, and the pair with the smallest LCM will have the most number of common multiples which are less than some number greater than the largest LCM.

LCM(3,4) = 12

LCM(3,5) = 15

LCM(3,6) = 6

LCM(4,6) = 12

Very well explained. thank you very much indeed.

 

[lookagain]

Since 6 is a multiple of 3, then all of the multiples of 6 will also be multiples of 3. There are 4 multiples of 6 less than 30. Actually, there are an infinite number of multiples of 6 less than 30.

In mathematics, a multiple is the product of any quantity and an integer. \(\displaystyle \ \ \ \ \ \)
Source: \(\displaystyle \ \ \ \)http://en.wikipedia.org/wiki/Multiple_(mathematics)

Which of the following pairs of numbers has the most number of positive common multiples which are less than 30?
(a) 3 and 4
(b) 3 and 5
(c) 3 and 6
(d) 4 and 6

There must be a clarifier, such as "positive" as suggested in the above quote box, or the word "nonnegative" (for a slightly different scenario), for example.

 

[MarkFL]

From the context of the problem and where it is posted, I felt it was obvious we were discussing positive integral multiples.