← Back to the activity

Grade 6 Math — 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.

01224364860

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.What is the LCM of 5 and 8?

  2. 2.What is the HCF of 12 and 18?

  3. 3.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?

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

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

  6. 6.Which of these is 60 written as a product of prime factors?

    • a) 4 × 15
    • b) 2 × 2 × 3 × 5
    • c) 2 × 5 × 6
    • d) 2 × 3 × 10

  7. 7.What is the LCM of 9 and 12?

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

Answer key — Grade 6 Math — HCF and LCM

  1. 1. 40
  2. 2. 6
  3. 3. 24
  4. 4. 1
  5. 5. 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
  6. 6. b) 2 × 2 × 3 × 5
  7. 7. 36
  8. 8. 6