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Year 7 Maths — HCF and LCM

Find the highest common factor and the lowest common multiple of two numbers, and use them to answer sharing and repeating problems.

Name: ________________________

Before you start

Every mark here is a multiple of 4 and a multiple of 6 at the same time. Move from one to the next.

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Zero is a multiple of everything, so it never counts. The first mark after it is 12, and that is what the LCM of 4 and 6 means — the earliest place their two lists of multiples meet.

  1. 1.Work out the LCM of each pair, then sort by whether it is below 30 or above 30.

    Groups: LCM below 30 · LCM above 30

    • 9 and 12
    • 3 and 8
    • 4 and 6
    • 5 and 8
    • 7 and 10
    • 6 and 9

  2. 2.One bell rings every 6 minutes and another rings every 8 minutes. They have just rung together. In how many minutes will they next ring together?

  3. 3.What is the LCM of 5 and 8?

  4. 4.What is the HCF of 7 and 13?

  5. 5.Two ropes are 12 cm and 18 cm long. Both are cut into equal pieces, as long as possible, with nothing left over. How long is each piece, in centimetres? Give just the number.

  6. 6.Match each pair of numbers to their HCF.

    • 6 and 9
    • 8 and 12
    • 10 and 15
    • 14 and 21
    • 16 and 24
    • 8
    • 3
    • 5
    • 4
    • 7

  7. 7.What is the HCF of 24 and 36?

  8. 8.Which pair of numbers has an HCF of 1?

    • a) 10 and 15
    • b) 8 and 12
    • c) 9 and 15
    • d) 8 and 15

Answer key — Year 7 Maths — HCF and LCM

  1. 1. 4 and 6 → LCM below 30; 3 and 8 → LCM below 30; 6 and 9 → LCM below 30; 5 and 8 → LCM above 30; 9 and 12 → LCM above 30; 7 and 10 → LCM above 30
  2. 2. 24
  3. 3. 40
  4. 4. 1
  5. 5. 6
  6. 6. 6 and 9 → 3; 8 and 12 → 4; 10 and 15 → 5; 14 and 21 → 7; 16 and 24 → 8
  7. 7. 12
  8. 8. d) 8 and 15