Most HCF and LCM puzzles are word problems. The skill is deciding which one you need: things that happen again and again and meet are about multiples (LCM); cutting or packing into the biggest equal groups is about factors (HCF).
✓ You passed this topic’s test.
How to solve it
Together again or cut equally? — “meeting again is a common multiple (LCM); cutting or sharing equally is a common factor (HCF)”
“Ring together again”, “smallest number both divide” → LCM: count in the bigger number until the smaller one divides it.
“Longest equal pieces”, “greatest number of identical packs” → HCF: list the factors and pick the greatest common one.
Check: the LCM is divisible by both numbers; the HCF divides both numbers.
Use it for: Bells, traffic lights, buses meeting again, cutting ribbons, packing gifts and tiling floors.
Worked example: Two bells ring every 12 minutes and every 18 minutes. They ring together at 9:00. After how many minutes will they next ring together? 36 min
They meet again at a common multiple of 12 and 18 — the smallest one is the LCM.
Count in 18s: 18, 36. 36 ÷ 12 = 3 exactly, so the LCM is 36.
Check: 36 = 12 × 3 = 18 × 2, and no smaller number (like 18 or 24) is divisible by both ✓
✏️ 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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🏁 Topic 8 test
20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.
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