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Grade 8 · Whole Numbers
HCF and LCM (Highest Common Factor & Lowest Common Multiple)
MEMORANDUM
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Mark
  / 10

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Find the HCF of 24 and 36.
    (2)
    24 = 23×3, 36 = 22×32 → shared 22×3 = 12✓✓ (2)
  2. 2
    Find the LCM of 8 and 12.
    (2)
    8 = 23, 12 = 22×3 → 23×3 = 24✓✓ (2)
  3. 3
    Find the HCF and LCM of 18 and 30.
    (2)
    18 = 2×32, 30 = 2×3×5 → HCF = 2×3 = 6; LCM = 2×32×5 = 90✓✓ (2)
  4. 4
    Two bells ring every 15 min and every 20 min. They ring together at 08:00. When do they next ring together?
    (2)
    LCM of 15 & 20 = 60 min → 09:00✓✓ (2)
  5. 5
    60 red and 48 blue beads are shared into identical packs (same reds per pack, same blues per pack) using as many packs as possible. How many packs?
    (2)
    Number of packs = HCF(60, 48). 60 = 22×3×5, 48 = 24×3 → HCF = 22×3 = 12 packs✓✓ (2)
TOTAL: 10 marks
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