Two whole numbers have a greatest common factor of 8 and a least common multiple of 48. Which of the following pairs of whole numbers will satisfy the given conditions?
F. 4 and 9
G. 5 and 10
H. 10 and 16
J. 14 and 20
K. 16 and 24
The correct answer is K.
You are given that both numbers have a factor of 8 and that they both factor into 48 evenly (48 is the least common multiple). Therefore, the following is true:
48 = 8 × a × b
Because 48 = 8×6, a×b must equal 6; a could equal 2 and b could equal 3, which means that one of the given numbers has a factor of 2 and the other has a factor of 3. Both numbers have a common factor of 8, so one number could be 8×2 = 16 and the other number could be 8 × 3 = 24.
Write something about yourself. No need to be fancy, just an overview.