Free Maths Calculator

HCF and LCM Calculator

Find the highest common factor and lowest common multiple of two numbers in one go. The calculator breaks both numbers into prime factors first, shows which factors are shared, then builds the HCF and LCM from them, the same method that earns full marks in GCSE and 11+ working.

Try It: Enter Your Numbers

Your question

Updates as you type

Answer

Method, Step by Step

    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 of 8 and 15.Show answerHide answer

    Answer: 1

    8 = 2 × 2 × 2 and 15 = 3 × 5 share no prime factors.