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Numbers - LCM (Lowest Common Multiple) and HCF - (Highest Common Factor)

These terms are not actually that hard to understand Just learn these simple facts:

The Lowest Common Multiple (LCM) is the SMALLEST number that will DIVIDE BY ALL the numbers in question.

E.g. 3, 6, 9, 12, 15 are all multiples of 3. 5, 10, 15, 20, 25 are all multiples of 5.

The lowest number that is in both lists is 15, so 15 is the LCM of 3 and 5.

The Highest Common Factor (HCF) is the BIGGEST number that will DIVIDE INTO ALL the numbers in question.

E.g. 1, 2, 4, 8 are all factors of 8. 1, 2, 3, 4, 6, 12 are all factors of 12. The highest number that is in both lists is 4, so 4 is the HCF of 8 and 12.

1 - Multiples and LCM

  1. List the first ten multiples of 6, starting at 6.
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  2. List the first ten multiples of 5, starting at 5.
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  3. What is the LCM of 5 and 6?
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X

2 - Factors. HCF (Highest Common Factor)

  1. List all the factors of 30.
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  2. List all the factors of 48.
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  3. What is the HCF of 30 and 48?
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X

3 - Find the HCF (Highest Common Factor)

For each set of numbers find the HCF.
I tell you what, it's a lot easier to find the LCM or HCF once you've listed the multiples or factors. If you miss this out it'll all go horribly wrong!
  1. 40, 60
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  2. 10, 40, 60
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  3. 10, 24, 40, 60
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  4. 15, 45
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  5. 15, 30, 45
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  6. 15, 20, 30, 45
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  7. 32, 64
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  8. 32, 48, 64
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  9. 16, 32, 48, 64
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X

4 - Find the LCM (Lowest Common Multiple)

For each set of numbers find the LCM.

  1. 40, 60
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  2. 10, 40, 60
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  3. 10, 24, 40, 60
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  4. 15, 45
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  5. 15, 30, 45
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  6. 15, 20, 30, 45
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  7. 32, 64
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  8. 32, 48, 64
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  9. 16, 32, 64
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X

5 - Find the LCM (Lowest Common Multiple)

Laura, Rita and Alan regularly go swimming. Laura goes every 2 days, Rita goes every 3 days and Alan goes every 5 days. They all went swimming together on Friday 1st June. This is just an LCM type question. Can you see why?
  1. On what date will Laura and Rita next go swimming together?
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  2. On what date will Rita and Alan next go swimming together?
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  3. On what day of the week will all 3 next go swimming together?
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X
  4. Which of the 3 (if any) will go swimming on 15th June?
    No such question type as Set qData['type'] to valid type. Eg "input" , "select" or "textarea" ... X

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