Math in Focus 4th Grade--help me with this problem :)

[umsami]

Here is a list of numbers. Circle the multiples of 5.  Two of the multiples of 5 are common multiples of 5 and X.  

 

4  5   7  10  15   24  25   27  35   42   45  49

 

What is X?

 

 

 

The answer is (according to the teacher's manual) 3 or 15.    What is their thought process?

 

I can work back and see it, but I'm not sure how to help my son do it.  We can list all the multiples of 5. (5, 10, 15, 20, 25, 30, 35, 40, 45)  But then how  do we figure out which are for X?

[EKS]

The only thing I can think of is that you know you're looking for a pair of numbers that have a second common factor (x).  The even multiples (10, 20, etc) all have the common factor 2, but there are four of them, not two.

 

It's a very strange problem.

[mom2bee]

1) List the multiples of 5: 5, 10, 15, 25, 35, 45.

 

2) Factor those multiples to see which have a common factor other than 5.

05 = 5 * 1

10 = 5 * 2

15 = 5 * 3

25 = 5 * 5

35 = 5 * 7

45 = 5 * 9  OR 5 * 3 * 3

 

Therefore both 15 and 45 are multiples of both 5 and 3, with 3 being x.

[umsami]

Thanks mom2bee. :)

[blondeviolin]

Your multiples of 5 are 15, 25, and 45.  Of those multiples, 15 and 45 are also multiples of 3 or 15.

[umsami]

"It's a very strange problem."

 

Thank you for making me feel better. :)