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 Solution: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.
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