If 9 and 12 each divide q without remainder which of the following must q divide without remainder?
(A) 1
(B) 3
(C) 36
(D) 72
(E) The answer cannot be determined from the given information.

Question

If 9 and 12 each divide q without remainder which of the following must q divide without remainder?
(A) 1
(B) 3
(C) 36
(D) 72
(E) The answer cannot be determined from the given information.

anonymous · Answer

You are basically being asked what is the LCM of 9 and 12 because 9 and 12 both go evenly into "q".  To find that LCM, construct a list of prime factors from both 9 and 12:

From 9:     3 x 3
From 12:   2 x 2 x 3

Construct a list that includes from both where you have the mnimum:

2 x 2 x 3 x 3     ->     36

anonymous · Answer

All good now, @thundermega ?

anonymous · Answer

Yes thank you..

anonymous · Answer

uw!  Good luck to you in all of your studies and thx for the recognition! @thundermega

anonymous · Answer

btw, 36 is merely the largest number that divides "q" without a remainder.  Of course, both "1" and "3" divide "q" without a remainder. @thundermega