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HCF and LCM by prime factorisation sheet
3-mark answer frame

Find the LCM and HCF of 120 and 252 by prime factorisation, and verify that LCM × HCF = product of the two numbers.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Write what is given and what is to be found. Numbers: 120 and 252. To find: HCF and LCM, then verify the product rule.
  2. 2 · Write the method. HCF = product of the smallest powers of common primes. LCM = product of the greatest powers of all primes.
  3. 3 · Factorise each number. 120 = 2³ × 3 × 5 and 252 = 2² × 3² × 7.
  4. 4 · Find the HCF and LCM.
    • HCF = 2² × 3 = 12
    • LCM = 2³ × 3² × 5 × 7 = 8 × 9 × 35 = 2520
  5. 5 · Verify.
    • HCF × LCM = 12 × 2520 = 30240
    • 120 × 252 = 30240
  6. 6 · Check and box the answer. HCF = 12, LCM = 2520. Since 30240 = 30240, LCM × HCF = product of the numbers is verified.

Scoring tip: Write the prime factorisations in power form side by side. Then the smallest and greatest powers are easy to pick.