Quantitative aptitude · lesson 2 of 30 · free

HCF and LCM word problems — Quantitative aptitude for kids

Bells that ring together again, runners who meet at the start, the biggest can that empties two tanks, the largest tile for a floor — every one of these is an HCF or LCM question in disguise. Decide which one, then use prime factors.

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The method

LCM or HCF? — “things that meet again → LCM; the biggest size that fits exactly → HCF”

  1. Bells, lights, runners “together again”: find the LCM of the gaps.
  2. Biggest can, rope piece or tile that fits exactly: find the HCF.
  3. Leaves the same remainder r every time: LCM + r.
  4. Number of tiles = (length ÷ tile side) × (width ÷ tile side).

Use it for: Timetables, traffic lights, cutting cloth or rope into equal pieces, tiling a floor, and HCF/LCM word problems in tests.

🧮 Check your own sums with the free HCF and LCM calculator — it shows the working.

Worked example: Three temple bells ring every 6, 8 and 12 minutes. They ring together at 9:00 am. After how many minutes will they next ring together? → 24

  1. 6 = 2 × 3, 8 = 2³, 12 = 2² × 3.
  2. LCM = 2³ × 3 = 24.

Check: 24 ÷ 6 = 4, 24 ÷ 8 = 3, 24 ÷ 12 = 2 — and no smaller number works for all three ✓

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✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

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🏁 Lesson 2 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ HCF and LCM Word Problems Worksheet

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