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The smallest fraction, which each of 6/7, 5/14, 10/21 will divide exactly is_________?

Correct answer: A. 30/7

  • A. 30/7
  • B. 30/98
  • C. 60/147
  • D. 50/294

Explanation

For the standard least-common-multiple interpretation of fractions, 30/7 works because (30/7) ÷ (6/7) = 5, (30/7) ÷ (5/14) = 12, and (30/7) ÷ (10/21) = 9, all whole numbers. Thus it is the least common multiple of the three fractions under the usual school convention. The likely mistake is choosing 30/98 by combining denominators without ensuring that division by every given fraction gives a whole number.

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