How to use the LCM and HCF calculator
- Type your numbers separated by commas or spaces, for example 24, 36, 60. You can enter 2 to 20 numbers.
- For fractions use a slash (3/4) and for decimals a point (0.6). The answer updates as you type.
- Read the HCF and LCM at the top, then the working below: copy whichever method your book or exam asks for.
Four ways to find the HCF and LCM
1. Prime factorisation
Break each number into primes. The HCF takes the primes every number shares, each to its lowest power; the LCM takes every prime that appears, each to its highest power. For 24 = 2³ × 3, 36 = 2² × 3² and 60 = 2² × 3 × 5: HCF = 2² × 3 = 12 and LCM = 2³ × 3² × 5 = 360.
2. Division (ladder) method
Write the numbers in a row and divide by a prime that goes into at least one of them, bringing down any number it doesn't divide. Keep going until every number is 1; the LCM is the product of the primes on the left. For the HCF, divide only by primes that go into every number; stop when no prime divides them all, and multiply the primes you used.
3. Euclid's division algorithm
Divide the larger number by the smaller and keep the remainder: a = b × q + r. Then divide b by r, and so on. When the remainder is 0, the last divisor is the HCF. NCERT's example, 4052 and 12576, takes seven divisions: 12576 = 4052 × 3 + 420, 4052 = 420 × 9 + 272, … 24 = 4 × 6 + 0, so the HCF is 4. With the HCF of two numbers, LCM = a × b ÷ HCF = 4052 × 12576 ÷ 4 = 12,739,488.
4. Listing factors and multiples
For small numbers, write out each list. Multiples of 6: 6, 12, 18, 24, 30, 36, 42; of 7: 7, 14, 21, 28, 35, 42; of 21: 21, 42. The first number in every list, 42, is the LCM. Factors work the same way for the HCF: the biggest number in every factor list. The calculator shows the lists when they are short enough to read (up to 20 multiples per number, and factors of numbers up to 10,000).
Worked example: 12 and 18
12 = 2² × 3 and 18 = 2 × 3², so the HCF is 2 × 3 = 6 and the LCM is 2² × 3² = 36. Check: 6 × 36 = 216 = 12 × 18. The common factors are the factors of the HCF: 1, 2, 3 and 6. The common multiples are the multiples of the LCM: 36, 72, 108 and so on.
Where you use LCM and HCF
- Adding fractions: the LCM of the denominators is the lowest common denominator, so 1/12 + 1/18 = 3/36 + 2/36 = 5/36.
- Simplifying fractions: divide the top and bottom by their HCF: 18/24 ÷ 6 = 3/4.
- Things that repeat: two bells ringing every 12 and 18 minutes ring together every 36 minutes (the LCM).
- Equal groups: the largest tile that fits a 240 cm × 360 cm floor with no cutting is 120 cm square (the HCF).
The calculator uses exact whole-number arithmetic, so the LCM of large numbers keeps every digit. Methods follow NCERT Class 10 Mathematics, chapter 1 (Real Numbers).