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Quantitative aptitude · lesson 1 of 30 · free

HCF and LCM — Quantitative aptitude for kids

The HCF (highest common factor) is the biggest number that divides two numbers exactly. The LCM (lowest common multiple) is the smallest number both divide into. Break each number into prime factors and both come out easily.

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The method

Prime factors — “break each number into primes — the shared ones make the HCF, all of them make the LCM”

  1. Write each number as a product of primes: 36 = 2 × 2 × 3 × 3.
  2. HCF: multiply the primes the numbers share (each as many times as it appears in both).
  3. LCM: take every prime the greatest number of times it appears.
  4. For two numbers, HCF × LCM = first number × second number.

Use it for: Simplifying fractions, HCF/LCM questions in Class 5–10 maths, and aptitude and scholarship tests.

🧮 Check your own sums with the free HCF and LCM calculator — it shows the working.

Worked example: Find the HCF of 36 and 48. → 12

  1. 36 = 2 × 2 × 3 × 3 and 48 = 2 × 2 × 2 × 2 × 3.
  2. They share 2 × 2 × 3 = 12.

Check: LCM = 36 × 48 ÷ 12 = 144, and 12 × 144 = 1728 = 36 × 48 ✓

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✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

✏️ Practice

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🏁 Lesson 1 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ HCF and LCM Worksheet

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