Free Maths Calculator

HCF and LCM Calculator

Find the highest common factor and lowest common multiple of two or three numbers in one go. The calculator breaks each number into prime factors, places them in a Venn diagram so the shared ones sit in the overlap, then builds the HCF and LCM from them, the method that earns full marks in GCSE and 11+ working.

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    Worked Example

    Find the HCF and LCM of 24 and 36.

    1. Prime factors:24 = 2 × 2 × 2 × 3 and 36 = 2 × 2 × 3 × 3
    2. The shared factors are 2, 2 and 3, so HCF = 2 × 2 × 3 = 12
    3. LCM = HCF × the leftover factors:12 × 2 × 3 = 72

    Answer: HCF = 12, LCM = 72

    Try These Yourself

    Find the HCF of 18 and 30.Show answerHide answer

    Answer: 6

    18 = 2 × 3 × 3 and 30 = 2 × 3 × 5. Shared: 2 × 3 = 6.

    Find the LCM of 6 and 8.Show answerHide answer

    Answer: 24

    Multiples of 8: 8, 16, 24. The first one that is also a multiple of 6 is 24.

    Find the HCF and LCM of 12, 18 and 30.Show answerHide answer

    Answer: HCF = 6, LCM = 180

    12 = 2² × 3, 18 = 2 × 3², 30 = 2 × 3 × 5. Fewest of each shared prime: 2 × 3. Most of every prime: 2² × 3² × 5.