Master HCF & LCM from Zero

Imagine you have 12 chocolates and 18 biscuits. You want to divide them into equal groups with nothing left over. The maximum number of groups you can make is 6 — and that is the HCF of 12 and 18. Now imagine one bus arrives every 12 minutes and another every 18 minutes. You want to know when both will arrive together. The answer is 36 minutes — and that is the LCM of 12 and 18. HCF (Highest Common Factor) is the largest number that divides two or more numbers exactly. LCM (Least Common Multiple) is the smallest number that is divisible by two or more numbers.

Key Formulas

Key Relationship

HCF × LCM = Product of the two numbers

This only works for TWO numbers. Very frequently asked in exams!

HCF of Fractions

HCF = HCF of Numerators / LCM of Denominators

Example: HCF of 2/3 and 4/9 = HCF(2,4) / LCM(3,9) = 2/9

LCM of Fractions

LCM = LCM of Numerators / HCF of Denominators

Example: LCM of 2/3 and 4/9 = LCM(2,4) / HCF(3,9) = 4/3

Numbers in Ratio

If numbers are in ratio a:b, then numbers = a×HCF and b×HCF

Example: Ratio 3:4, HCF = 5 → Numbers are 15 and 20

⚡ Shortcut Tricks

HCF × LCM = Product of two numbers. If you know any three values, you can find the fourth instantly.

Co-prime numbers have HCF = 1. Their LCM = their product. Example: HCF(8,9) = 1, LCM(8,9) = 72.

HCF of numbers can never be greater than the smallest number in the group.

LCM of numbers can never be less than the largest number in the group.

If one number divides the other exactly, then HCF = smaller number and LCM = larger number. Example: HCF(6,12) = 6, LCM(6,12) = 12.

For 'least number divisible by a, b, c' → find LCM(a,b,c). For 'greatest number that divides a, b, c' → find HCF(a,b,c).

✏️ Solved Examples

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