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Finding Common Ground

Which one does the question want?

Cut ribbons into equal pieces. Or find when two buses leave together. Which one needs the HCF?

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Ask what the number must do.
Step 1 of 3
  1. Ask what the number must do.
  2. Ribbon: go into both 12 and 18 → HCF = 6.
  3. Buses: 12 and 18 must go into it → LCM = 36.

One question, asked of the answer

Cutting the ribbons needs the HCF. The buses need the LCM.

Ask what the answer must do. Does it go into both numbers? You need the HCF. Do both numbers go into it? You need the LCM.

What the answer must do, in four situations
SituationWhat the answer must doWhich one
Cut 12 m and 18 m ribbons into equal piecesGo into 12 and into 18HCF, 6
Buses leave together now, then every 12 and 18 minutesHave 12 and 18 go into itLCM, 36
Put 8 and 15 players in equal rows, teams not mixedGo into 8 and into 15HCF, 1
Lamps blink together now, then every 4 and 6 secondsHave 4 and 6 go into itLCM, 12

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This track

  1. 0 Start here
  2. 1 The primes inside a number
  3. 2 A factor tree, and where it ends
  4. 3 The biggest one they share
  5. 4 Reading it off the two prime lists
  6. 5 When two step counts meet
  7. 6 The same two lists, read the other way
  8. 7 Which one does the question want?
  9. 8 Check it before you hand it in
  10. 9 Co-prime numbers
  11. 10 One table for the HCF and the LCM
  12. 11 The HCF, the LCM and the product
  13. 12 Checkpoint
  14. 13 The big picture
  15. 14 Track quiz

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