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Finding Common Ground

When two step counts meet

A market bus leaves every 12 minutes. A station bus leaves every 18 minutes. Both leave together at 0.

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Steps of 12: 12, 24, 36.
Step 1 of 4
  1. Steps of 12: 12, 24, 36.
  2. Steps of 18: 18, 36.
  3. Both reach 36.
  4. LCM(12, 18) = 36.

Two lists, and where they touch

The buses leave together again at minute 36.

Counting in 12s gives the multiples of 12: 12, 24, 36. Counting in 18s gives 18, 36.

A number on both lists of multiples is a common multiple. The lists first have 36 in common. That is the lowest common multiple, or LCM.

LCM(12, 18) = 36 means: the LCM of 12 and 18 is 36.

Multiples of 4 are 4, 8, 12. Multiples of 6 are 6, 12. They first share 12. So LCM(4, 6) = 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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