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CTET PAPER II 2019 · PYQ · HCF and LCM · medium

If x = 2³ × 3² × 5³ × 7³, y = 2² × 3³ × 5⁴ × 7³, and z = 2⁴ × 3⁴ × 5² × 7⁵, then H.C.F. of x, y and z is

  1. A.(30)² × 7³✓ Correct
  2. B.(15)³ × 7⁴
  3. C.(30)³ × 7³
  4. D.30 × 7⁵

Explanation

HCF is found by taking the lowest power of each common prime factor. For 2: min(3,2,4) = 2, for 3: min(2,3,4) = 2, for 5: min(3,4,2) = 2, for 7: min(3,3,5) = 3. So HCF = 2² × 3² × 5² × 7³ = (2×3×5)² × 7³ = (30)² × 7³.
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